Gemara

(Mishnah): If Reuven extinguished a Ner because he fears lest Nochrim or bandits see it [and harm him], due to melancholy [when he can see], or to enable a Choleh (sick person) to sleep, he is exempt.

If he extinguished to save the Ner [from breaking], or to save oil or the wick, he is liable.

R. Yosi exempts in every case, except for saving the wick, for he makes a singed wick.

Question: The middle clause obligates [for Melachah she'Einah Tzerichah l'Gufah], like R. Yehudah. What is the case in the Reisha?

If the Choleh is in mortal danger, it should not say 'exempt'. It is permitted!

If he is not in mortal danger, Reuven is Chayav Chatas!

Answer: Really, he is in mortal danger, and it should say 'permitted'. It says 'exempt' for parallel structure with the Seifa, which says 'Chayav'.

(R. Oshaya - Beraisa): One may not extinguish a Ner to enable a Choleh to sleep. If one did so, he is exempt.

The case is, there is no mortal danger. It is like R. Shimon.

31b - Question: Whom does R. Yosi hold like [regarding Melachah she'Einah Tzerichah l'Gufah]?

Answer #1 (Ula): He holds like R. Yehudah. He obligates for Soser (destroying) only if he intends to build in the same place. (Then, the Stirah is constructive. Likewise, extinguishing makes a better wick, but it does not improve the Ner or oil.)

Answer #2 (R. Yochanan): He holds like R. Shimon. A wick is different, like Rav Hamnuna taught:

i. (Rav Hamnuna): The case is, the wick needs to be singed. (It was not singed before Shabbos.) R. Shimon admits that one is liable, for this makes a Kli.

Support (Rava): It says 'for he makes a singed wick.' It does not say 'for it becomes a singed wick (i.e. due to Binyan, even if it was singed before Shabbos).'

42a: Shmuel holds that we may extinguish (on Shabbos) a metal coal in Reshus ha'Rabim, in order that people will not be harmed, but not a coal of wood.

Question: If he holds like R. Shimon, he should permit extinguishing even a wooden coal!

Answer: He holds like R. Shimon regarding Davar she'Eino Miskaven, but he is Mechayev for Melachah she'Einah Tzerichah l'Gufah like R. Yehudah.

157a (Rav Acha or Ravina): Regarding all laws of Shabbos, the Halachah follows R. Shimon, except for Muktzeh due to Mi'us, e.g. a used lamp;

(The other of Rav Acha and Ravina): The Halachah follows R. Shimon even regarding Muktzeh due to Mi'us, but not regarding Muktzeh due to Isur, e.g. a lamp in which a fire was burning at the start of Shabbos;

Rishonim

Rambam (Hilchos Shabbos 1:7): Anyone who does Melachah on Shabbos is liable, even if it is Einah Tzerichah l'Gufah. E.g. if he extinguishes a Ner because he needs the oil or wick, lest it be lost or burned or lest the lamp break, he is liable. Extinguishing is a Melachah, and he intended to extinguish. Even though he does not need the extinguishing itself, and he did so only for the sake of the oil or earthenware or wick, he is liable.

Ra'avad: R. Chananel rules like R. Shimon, since Rava rules like him.

Magid Mishneh: It seems that the Rif rules like Shmuel, who holds like R. Yehudah. Rav hlolds that R. Yehudah regarding this, and obligates even Davar she'Eino Miskaven. Shmuel argues about Davar she'Eino Miskaven and permits it. It is unreasonable to be lenient about both of these. However, Acharonim are lenient about both. The Ramban and Rashba struggle to say that the Rif rules like R. Shimon.

i. Ran (DH d'Amar): We hold like R. Shimon, who exempts Melachah she'Einah Tzerichah l'Gufah. The Rif brought Shmuel's teaching, that one may extinguish a metal coal, but not a wooden coal. We established it like R. Yehudah. The Rif did not intend to rule like R. Yehudah, for he brought [the Seifa] of the Mishnah of extinguishing, which we establish like R. Shimon! He also brought trapping a snake and piercing an abscess, which we establish like R. Shimon. He brought Shmuel's teaching to teach that since we rule like R. Shimon, one may extinguish even a wooden coal. The Ramban holds like this. The Rambam rules like R. Yehudah, that one is liable for Melachah she'Einah Tzerichah l'Gufah.

i. Ran (67b DH v'Yesed): The Gemara said that in all of Shabbos, the Halachah follows R. Shimon. The Ramban derives that this includes Melachah she'Einah Tzerichah l'Gufah. We cannot say that we rule like him only regarding Muktzeh. One opinion holds that we do not rule like R. Shimon regarding four kinds of Muktzeh, i.e. due to Mi'us, Isur, Chisaron Kis, and dry figs and raisins. If so, why did we say that the Halachah follows him in all of Shabbos?! Also, according to the opinion that excludes only Muktzeh due to Isur, [if we rule like R. Shimon only regarding Muktzeh,] we should have said that the Halachah follows R. Meir [who forbids only Muktzeh due to Isur]! Rather, we rule like R. Shimon in all of Shabbos.

Poskim

Shulchan Aruch (OC 278:1): One may extinguish a Ner in order to enable a dangerously sick Choleh to sleep.

Beis Yosef (DH ha'Mechaveh): The Tur rules like R. Shimon, like the Ramban.

Beis Yosef (DH v'Im): Singing the wick makes it catch fire better the next time. Those who rule like R. Shimon hold that the Halachah follows R. Yosi. Those who rule like R. Yehudah hold that the Halachah does not follow R. Yosi.

Taz (1): If there is danger due to bandits or sickness, it is permitted.

Magen Avraham (1): Tosfos (94a DH R. Shimon) says that if a Melachah is not needed for the same purpose as in the Mishkan, it is Einah Tzerichah l'Gufah.

Mishnah Berurah (1): Perush ha'Mishnayos permits only if they cannot move the Choleh elsewhere, or to block the light, e.g. through covering it with a Kli, or moving the lamp to another room. Surely it is better to move Muktzeh than to extinguish!

Mishnah Berurah (2): When he wakens later, one may light the Ner for him. If a Nochri is available and can do these matters without delay, we do through him.

Bi'ur Halachah (DH Lichvos): It seems that even the Rambam permits only to light a lamp so the Choleh will not be in the dark, but one may not tilt the lamp so it will burn better. One may transgress Shabbos only for what is essential.

Mishnah Berurah (3): It is permitted also if there is danger due to bandits and there is no way to hide the light without extinguishing it. We permit also for a Choleh with Safek danger, but not if there is no danger, even according to the Poskim who exempt extinguishing due to Einah Tzerichah l'Gufah. It is forbidden mid'Rabanan. The same applies to other Melachos in which one does not need the Melachah itself, e.g. he digs a hole, and he needs only the earth. Extinguishing is more stringent than other Isurim mid'Rabanan, for sometimes one is liable for it, e.g. he extinguishes wood to make coals, or singes a wick

Bi'ur Halachah (DH Mutar): The Me'iri connotes that even though one could make a barrier to block the light, one may extinguish for a dangerously sick Choleh, even according to R. Yehudah. One could reject this. The Rambam holds that if there is another solution, he is Chayav Chatas for extinguishing. If not, the Gemara could have established the Mishnah to discuss such a case, and this is why he is exempt, but it is not permitted! This is only because the Rambam obligates for Melachah she'Einah Tzerichah l'Gufah. The Poskim who exempt, perhaps they permit for a dangerously sick Choleh. Do not support my reasoning from the fact that the Gemara did not establish R. Oshaya's Beraisa like R. Shimon, and it discusses a dangerously sick Choleh when there is another solution. Perhaps the Gemara prefers to teach that it is forbidden l'Chatchilah for a Choleh without danger. In practice, all agree that one should be stringent when there is another solution, e.g. to cover the light. Extinguishing is more stringent than other Isurim mid'Rabanan, which a Yisrael may do for a Choleh without danger. Also, the Rambam obligates a Chatas, so we should not be lenient.

Kaf ha'Chayim (6): Also, we are more stringent about extinguishing, for not everyone knows the difference between Melachah she'Tzerichah l'Gufah and she'Einah Tzerichah l'Gufah. This is why we forbid telling a Nochri to extinguish.

Bi'ur Halachah (DH Bishvil): Seemingly, it does not depend on whether there is danger [now], rather, on whether inability to sleep will bring to danger! I saw an opinion explain the Gemara and Shulchan Aruch like this. I say that they connote unlike this. Sleep is good for a Choleh. We assume that this can help cure him, or at least extend his life somewhat. Perhaps lack of sleep will increase the danger. However, even if there is no danger, if the doctor says that lack of sleep will aggravate the illness and he can come to danger, it is permitted. The Shulchan Aruch teaches that Stam it is permitted for a dangerously sick Choleh.

Bi'ur Halachah (DH ha'Choleh): All forbid for a Choleh without danger. Do not ask why we permit extinguishing even a wooden coal in Reshus ha'Rabim so people will not get hurt. We are more lenient for pain to the Rabim than for one Choleh.

Kaf ha'Chayim (1): In 316:8, the Shulchan Aruch rules like R. Shimon, and mentions the Rambam's opinion as secondary. Therefore, if one did a Melachah she'Einah Tzerichah l'Gufah b'Shogeg or b'Mezid and seeks a remedy, we are not as stringent as for one who did a Melachah she'Tzerichah l'Gufah.

Kaf ha'Chayim (4): Tal Oros says that if one lit a lamp during the day, which is needless and he does not benefit from it, even so R. Yehudah exempts. This is burning destructively. He brought Chavos Ya'ir, who says that he is liable, but he disagreed. A case occurred in which someone lit a Yartzite candle before Shabbos, and in the morning saw that it extinguished, and totally b'Shogeg relit it. He needs Kaparah like a Mechalel Shabbos b'Shogeg. This is not destructive, for he intended for Iluy Neshamah.