For whom is this sign?
Rashi: It is for Chizkiyah. Even after Sancheriv fell, they feared starving to death.
What is the sign?
Rashi: When you see the hordes (Sancheriv's army) fall, that is a sign that also the promise of food will be fulfilled.
Rashi (Yeshayah 37:30), from Targum Yonasan: When you see Sancheriv return to his land and fall 1 , you will know that the second promise [about what you will eat] will be fulfilled.
Radak: The first Nevu'ah was that Sancheriv will hear [about Melech Kush] and return to his land. You know that it was fulfilled from Sancheriv's second message to you. Also the Nevu'ah "Bazah Lecha
I.e. after Hashem wipes out his camp, he returned to his land and his sons killed him. I do not see how our text of Yonason hints to this. (PF)
What will they eat in the coming years?
Rashi: The first year they will eat vegetation, and the second year, cut trees will sprout.
Radak: They knew that the first year they will eat Sefichim (what grows by itself), for they had not seeded. The Chidush was this it will be blessed, and it will suffice for them. The second year, they will eat Sachish (what grew from what fell from the Sefichim). The third year they will plant what was left over from the Sachish, and reap without fear of enemies.
Why does it say here "Sachish", and in Yeshayah 37:30, "Shachis"?
Radak (Yeshayah 37:30): These are the same, just the letters are re-arranged, like Kesev and Keves, Salmah and Simlah.
QUESTIONS ON RASHI
Rashi writes that even after Sancheriv fell, they feared starving to death. What is the reason?
Rashi: Sancheriv destroyed the land and cut the trees. 1
Radak: They had not seeded the land that year, due to Sancheriv's army.
Radak citing Seder Olam 23: Sancheriv came two weeks before Pesach, so they could not seed 2 .
There should have been plenty of food from the spoils of Sancheriv's army, like after Aram fled from Shomron (7:18)! There were less than 260,000 men in Yerushalayim. Shevna expounded in front of 130,000 people, and they were the majority (Sanhedrin 26a). Presumably, there were less than 1,000,000 people in all. Ashur had at least 370,000,000 soldiers (refer to 18:24:1:1). If they destroyed the land, surely they had rations to eat during the siege. Each Jew could survive on the rations of 370 soldiers for a long time! Perhaps the rations were perishable, and would not last until the land could produce. (PF)
They could seed only after his camp died, on Pesach, so the grain was permitted only after offering the Omer a year later. Therefore, the Navi tells what they will eat, b'Heter. This does not explain why there was mortal danger. Piku'ach Nefesh overrides Chadash and other Isurim! Normally, people sow at the beginning of winter (Bava Metzi'a 106b). Perhaps this year they did not, for they expected Ashur's army to return, just like Chizkiyah closed the springs. However, this does not show that he was adamant that they not find food in the land. Armies normally take food for themselves, but not water! (PF)