Gemara

(Rav): The Halachah follows R. Yehudah, who forbids Davar she'Eino Miskaven (an action that may result in an Isur for which one does not intend);

(Shmuel): The Halachah follows R. Shimon, who permits it.

Shabbos 43a (Beraisa): On Shabbos, one may spread a mat over a hive, to protect it from the sun or rain, as long as he does not intend to trap (the bees).

The case is, he intends for the sake of the honey inside. (It is not Muktzeh.)

Question: Who is the Tana of the Beraisa?

R. Shimon would not require intent for the honey. He permits (most categories of) Muktzeh)!

R. Yehudah (who forbids most kinds of Muktzeh) would forbid even without intent to trap. He forbids Davar she'Eino Miskaven!

Answer: It is R. Yehudah. It means that he spreads the mat in a way that it will not trap, i.e. he leaves room for the bees to leave.

Beitzah 36a - Question: The Beraisa is like R. Yehudah, who forbids Muktzeh. The Seifa permits 'as long as he does not intend to trap.' This is like R. Shimon, who permits Davar she'Eino Miskaven!

Answer: The Seifa is not like R. Shimon. Even he forbids a Pesik Reishei (an inevitable consequence)!

Rather, it is R. Yehudah. The case is, there are Kavei (openings for the bees to leave);

The Beraisa means that he spreads the mat in a way that it does not trap.

Question: Obviously, this is permitted!

Answer: One might have thought one may not trap species that are normally trapped, but one may trap species that are not normally trapped. The Beraisa teaches that this is not so.

Rishonim

Rambam (Hilchos Shabbos 10:25): On Shabbos one may spread a mat over a hive to protect it from sun or rain, as long as he does not intend to trap, for he may take it whenever he wants. (I.e. it is still permitted to move the mat.)

Magid Mishneh: It is not a surety that the bees will be trapped. If not, it is forbidden even if he does not intend. Rather, it is possible that they will be trapped, and it is possible that they will escape.

Tosfos (36b DH Ela): Rashi explains that one may not cover all the holes. R. Yehudah would forbid this, and R. Shimon would permit. Also, initially it seems that if it is like R. Shimon, it is in any case (even if he traps the bees). This is difficult, for also R. Shimon forbids a Pesik Reishei! R' Moshe mi'Ivra says that also R. Shimon explains that there is a hole for bees to escape, but it is not visible (to the bees). Therefore, it is not a Pesik Reishei. R. Shimon permits, and R. Yehudah forbids even Davar she'Eino Miskaven. R. Yehudah requires a big hole, so the bees see how to leave.

Tur (OC 316): If one trapped a species that people do not trap, he is exempt, but it is forbidden. Therefore, Sefer ha'Terumah forbids locking a box in which there are flies. Rather, he leaves a knife or something else to hold the cover slightly open so they can escape. It seems to me that one need not be meticulous about this, for flies are not trapped in a box. If one will open it and (try to) seize them, they will flee. This is unlike bees in a hive. A Beraisa permits spreading a mat over it, as long as he does not intend to trap, for it is small and they are trapped in it. Also, regarding a hive it says 'as long as he does not intend to trap', which implies that if he does not intend, it is permitted.

Poskim

Shulchan Aruch (OC 316:3): If a species is not trapped, one who traps it is exempt, but it is forbidden. Therefore, even though people do not trap flies, one may not trap them.

Magen Avraham (6): One is exempt even if he traps them for a need.

Rema: Therefore one must be careful on Shabbos not to close a small box in which there are flies, for it is a Pesik Reishei that they will be trapped there.

Beis Yosef (DH v'Chasav Ba'al): Sefer ha'Terumah forbids to lock a box in which there are flies. The Mordechai (Shabbos 318) brings this, and the Agur (471) brings it in the name of Tosfos. The Beraisa in Shabbos 43a connotes like this. Tosfos and the Magid Mishneh explain that it is not certain that he will trap the bees. The Tur rejected Sefer ha'Terumah due to the Beraisa, which says 'as long as he does not intend to trap.' This is no rejection, for it cannot be that they will surely be trapped, for if so it is a Pesik Reishei! The Tur distinguishes between a hive, which is small, and a box. If so, we can distinguish between small and big boxes, and between big and small hives! Rather, if one can reject Sefer ha'Terumah, it is because the hive is a place in which they are trapped. This is like entering a lion into its cage. A box or hive is not where we trap flies. Perhaps flies are not considered trapped until one holds them in his hand.

Rebuttal (Taz 3): If the Beis Yosef rejected the Tur's rejection, surely this is no rejection! A lion in its cage is different, for it stays there and does not get angry and destroy its enclosure. If it is trapped elsewhere, it gets angry and destroys its enclosure, like Rashi says (Shabbos 106b DH ha'Tzad). Flies are different. They cannot leave the box. We must say that they are not trapped because when he opens it, they escape. The Tur holds like this.

Note: Perhaps the Beis Yosef means that 'the hive is a place in which they are trapped', i.e. one who traps bees (to bring them to another place or sell them) wants them in a sealed hive. If one wanted to trap a fly (e.g. for an experiment), he would want to be able to hold it in his hand.

Beis Yosef (ibid.): Alternatively, R. Shimon forbids spreading a mat in a way that is a Pesik Reishei only regarding bees, which is a species that is trapped. People do not normally trap flies, so it is permitted as long as he does not intend to trap, even though it is a Pesik Reishei.

Rebuttal (Taz 3, citing the Bach DH Od): Beitzah 36b connotes that bees are not a species that is trapped, and even so it is forbidden if it is a Pesik Reishei.

Beis Yosef (ibid.): In any case, since Sefer ha'Terumah forbids and the Mordechai brought it, and we do not see anyone who disagrees, who will be lenient and ignore their words?!

Gra (DH v'Lachen): The stringent opinion equates flies to bees.

Magen Avraham (7): The Rema holds that all permit a big box. Even if a man were inside, one could not seize him in one swoop.

Mishnah Berurah (15): Also, we are lenient about a big box because flies are not a species that people trap.

Kaf ha'Chayim (24): The Levush omitted 'small'. He forbids even a big box. Kolbo forbids closing a box with food, for there are often flies inside, unless there is an opening for them to flee.

Rema (ibid.): Some are lenient in a place that if he opens the box to take them, they will flee.

Taz (3): The Tur is correct. He did not totally permit. He said 'we need not be meticulous about this.' Also he forbids if one sees flies in the box. Rather, one need not be meticulous to check whether there are flies. Firstly, even if it is a Pesik Reishei because the flies have no place to leave, it is permitted, for it is not called trapped, for it is not sure that they will come to his hand. Perhaps when he opens the cover and wants to take them, they will flee and he will not get even one. This is unlike bees in a hive. The hive is small and bees are trapped in it. I.e. every hive is small regarding this. They cannot all flee. They are big, and fill the hive. Surely he will seize at least one! Flies are small. Usually, one who opens a box with flies cannot catch even one. This answers the Beis Yosef's question against the Tur.

Taz (3): The Tur's second question was that even if there are surely flies inside, they are not considered trapped like bees are. Even if you will say (unlike we said above) that it is a Pesik Reishei and forbidden, if it is a Safek whether there are flies inside, it is not a Pesik Reishei. We permit Davar she'Eino Miskaven, just like a hive when it is not a Pesik Reishei, e.g. there is a small hole. The Tur does not argue with Sefer ha'Terumah. He just teaches that one may close a box without checking for flies. The Halachah follows this in practice. One may rely on the Tur, for we do not find anyone who disagrees. The Bach explains the Tur to say that it is not a Pesik Reishei regarding bees, for he does not want them to be trapped, for then they cannot eat flowers and make honey. This is wrong. Surely, anything that is not normally trapped, he is not pleased to trap it, but Chachamim decreed due to species that people trap, which a person desires.

Bi'ur Halachah (DH v'Lachen): The Taz teaches a Chidush. Just like R. Shimon permits Davar she'Eino Miskaven when it is unsure if an act will occur (e.g. if dragging a bench will make a furrow), he permits when it is a Safek if the act is Asur (perhaps there are flies inside). Reasoning would forbid this like a Safek mid'Oraisa. However, Tosfos (Kesuvos 6a DH Hai) supports the Taz. He says that if one removes berries and makes a myrtle branch Kosher, but is unsure whether he will need it for the Mitzvah, this is not a Pesik Reishei. However, that depends on the future. Here, if there is something inside that people trap, he Vadai transgresses! People do not trap flies, so in any case it is a Safek mid'Rabanan and permitted. The Taz permits even to lock a house if he is unsure whether a deer is inside. A proof for the Taz is from Milchamos Hash-m (Shabbos 19b). He says that pouring cold water into a hot empty pot is not a Pesik Reishei of Tziruf (solidifying the pot), for perhaps Tziruf already occurred. The Me'iri says similarly.

Taz (4): Surely one may be lenient if he is unsure whether there are flies inside, especially since this is a mid'Rabanan matter, since this is not a species that people trap. It is only a decree lest one trap species that people trap. One chases out what he sees, and he need not worry lest there are others inside.

Magen Avraham (8): The Tur is lenient, even though he forbids a small hive. The Bach is stringent. This is primary.

Kaf ha'Chayim (26): Eliyahu Rabah says that in summer, one may not be lenient about a Safek regarding a box used for food (since almost surely there are flies). He says that the Agudah says so in Beitzah.

Bi'ur Halachah (DH v'Yesh): The Pri Megadim (9) is more lenient if there is food in the box, for then he is upset if flies are there. We are more lenient about a Pesik Reishei d'Lo Nicha Lei (that upsets him).

Gra (DH v'Yesh): The Tur is lenient, for a hive is different. Bees are trapped in it, i.e. even when one opens it. Even regarding bees, it is forbidden only if he intends. He holds like the Sugya in Shabbos. The Sugya in Beitzah connotes that there is no difference (between flies and bees).

Mishnah Berurah (14): One must leave a knife or something else to hold the cover slightly open so they can escape. Alternatively, it suffices if there is a small hole in the box, even if it is not blatant to the flies, for it is not a Pesik Reishei.