Gemara

Question (Rav Chisda): If Reuven lived in Shimon's yard without Shimon's Da'as (knowledge or consent), must he pay rent?

If the yard is not normally rented, and Reuven does not normally rent a place, Reuven didn't benefit, and Shimon didn't lose (surely, Reuven is exempt)! If the yard is normally rented, and Reuven normally rents a place, Reuven benefited and Shimon lost (surely, Reuven must pay)! Rather, he asked about a yard that is not normally rented, and Reuven normally rents a place.

20b - Answer #1 (Rami bar Chama - Mishnah): (If an animal ate food in Reshus ha'Rabim, it is exempt.) If it benefits, it pays the benefit.

Rebuttal (Rava): There, the damager benefits, and the owner of the food loses. Rav Chisda asked about when Reuven benefits and Shimon does not lose!

Rami bar Chama assumes that one who left food in a Reshus ha'Rabim made it Hefker (so also he does not lose).

Answer #2 (Mishnah): If a house fell, and Shimon (who owns the upper story) wants to rebuild it but Reuven (who owns the ground floor) refuses, Shimon may build (the ground floor) and live there until Reuven pays Shimon's expenses.

(Inference): Reuven does not deduct the benefit Shimon had from living there in the meantime. This shows that when Shimon benefits from Reuven, and Reuven does not lose, Shimon is exempt!

Rejection: There is different, for the owner of the ground floor is obligated to provide a basis for the upper story.

Answer #3 (Reisha - R. Yehudah): Even in this case, one who lives in another's yard without his knowledge must pay rent.

Inference: When Shimon benefits from Reuven, and Reuven does not lose, Shimon must pay!

Rejection: There, Reuven loses. Living in a new house blackens the walls.

21a (Rav Sechorah): If Levi lived in Yehudah's yard without Yehudah's Da'as, he need not pay. We learn from "desolation breaks the gates." (It benefits Yehudah if someone is there!)

A man built a house on a ruin of orphans. Rav Nachman collected it from him.

Inference: He holds that one who lives in Reuven's yard without Reuven's Da'as must pay Reuven.

Rejection: No. Originally, other people were living there and paying a modest rent to the orphans. Rav Nachman told the man to appease the orphans. He didn't, so Rav Nachman collected the house from him.

Rishonim

The Rif (9a) brings the episode with the man who built on orphans' ruins.

Nimukei Yosef (9a DH b'Tzivi): If Yehudah used his house for wood and straw, Levi must pay for blackening the walls. He need not pay more. Rav Nachman initially required the man who built a house on orphans' ruins to pay just a small amount, i.e. their loss. If Yehudah's house was not being used at all, Levi benefits him (by preventing its ruin) more than he harms, so he is totally exempt. The Rosh and Ritva say that if he caused any loss at all, he must pay all his benefit. The answers about one who built a wall on the fourth side (after his neighbor built walls around him on three sides) and paying rent due to blackening of walls support them.

Rosh (2:6): Before the man built on the orphans' ruin, others were living there and paying a modest rent, for there was no proper dwelling, just mere tents. The orphans could not pay for what he built. Rav Nachman told the man to appease the orphans with something. He didn't, so Rav Nachman collected the house until he gave a proper price for a ruin on which to build a house. This was more than the first residents were paying. Since the orphans lost something, he needed to pay all his benefit. Similarly, one who lives in a new house must pay all his benefit, for he blackens the walls.

Magid Mishneh (Hilchos Gezeilah 3:9): The Meforshim say that if there was any loss at all, e.g. he blackened the walls and decreased the value, even if it is not normally rented, Levi must pay everything. The Gemara confirms this.

Poskim

Shulchan Aruch (CM 363:7): Some say that when the yard is not normally rented and Levi is exempt, if there was any loss at all to the house, even a small loss, e.g. it was new and he blackened the walls, Levi pays full rent according to his benefit.

Beis Yosef (DH u'Mah she'Omar v'Im): The Rashba derives this from the two-story house that fell, and from the house built on orphans' ruins.

Gra (20 and 375:16): Tosfos (20b DH Ta) explains that (when Shimon rebuilt one story and lived there,) Chachamim argue with R. Yehudah (and exempt him from paying rent) only because the house is obligated to support the second story. If not, he would pay full rent, due to a small loss to Reuven (blackening the walls)! The Rashba says that the man who built on orphans' ruins did not need to pay more than their loss (the rental they used to receive). We hold like Tosfos, who obligates paying his entire benefit.

Panim Me'iros (1:62): R. Yehudah requires Shimon to build both stories. Rashi says that if he benefits from Reuven, this is like Ribis. Tosfos says that he builds both stories and lives in the Aliyah, for if he lives below he benefits (he saves walking up to the Aliyah) and Reuven loses (the walls blacken). This is like Tosfos holds in Bava Kama, that even if Reuven loses, Shimon is liable only if he benefited. The Ran always exempts for living in a yard not normally rented, for being settled outweighs the blackening of the walls. R. Yehudah holds that since Reuven would not have built yet, guarding his house does not benefit him, therefore Shimon must pay if he lives there, due to blackening. This applies to any house, even if it is old. The Rosh says that blackening is only in a new house. This is difficult.

SMA (8): The Shulchan Aruch (Sa'if 3) exempts a thief who used the animal he stole but did not weaken it. Perhaps we are not concerned for weakness from which it will recover. Alternatively, since he benefited, he is liable even for weakness that will recover, similar to one who lived in a house and blackened the walls, even though the walls can be whitened again.

Rema: If so, if Levi does not normally pay rent, he is exempt, for he did not benefit. Some disagree.

Source: R. Yerucham, in Beis Yosef (ibid.): If the yard is not normally rented, and Levi does not normally rent a place, some obligate and some exempt.

SMA (19): Since we force him to pay all his benefit, if he did not benefit he need pay only the loss he caused.

Gra (18): Rami bar Chama proved from the Mishnah that even though the victim loses, the damager is liable only if he benefited. Rava agreed that Levi is liable for Yehudah's loss only if Levi benefits. However, Rav Chisda asked about when Levi benefits and Yehudah does not lose!