Bava Kamma, Chapter 10, Mishnah 8. The Mishnah seeks to clarify one question: a thief who returned the item he stole, but did not inform the victim that the item was returned to its place - is this considered fulfilling the obligation of returning a stolen object?
The practical difference:
The practical difference is that if the return is not considered a valid return, the thief continues to bear responsibility for the stolen item. A person who borrows an item from his friend receives all the benefit of the loan, and therefore he is liable not only for theft and loss, but even for unavoidable accidents - circumstances beyond his control: you borrowed it, you are expected to return it. A thief is no less liable than one who takes without permission, and therefore he bears full responsibility. The meaning of this is: if he did not fulfill his obligation, and something happened to the item - it broke, died, was stolen, or anything similar - the thief will be obligated to pay its value.
The answer: It depends on the owner's knowledge:
The foundation of this matter is that a person watches over his belongings. Everything depends, therefore, on the question of whether the owner knew about the theft:
The owner knew it was stolen: Since he thought his belongings were no longer in his possession, he ceased watching over them. Once the item is returned, the owner does not know that he must resume watching over it, and he cannot be expected to guard what he does not know is in his possession. Therefore, the responsibility remains on the thief.
The owner did not know it was stolen: His guarding continued as usual, and when the item was returned, he continues to watch over it as he always did. There is, therefore, no reason why he should not resume being the responsible party, and the one returning it has fulfilled his obligation and is exempted from responsibility.
The difference between an inanimate object and an animal:
All of this applies to inanimate objects. One who steals a cup and returns it to the shelf: if the owner knew it was stolen and did not know it was returned - the thief is still responsible for it, since they did not activate the guarding system for the cup. And if they did not know at all that it was stolen - the guarding in the house operates just as it always did, and the thief is henceforth exempt from his responsibility.
But for an animal, the law is different. One who steals a sheep from his friend - the very fact that he removed it from the owner's domain, that it saw the wider world and was treated differently, is liable to change its behavior. Perhaps it will start to wander, having discovered that there is greener pasture outside the place where it is kept and guarded, and so forth. Because of this, it is not enough that the owner does not know that it was taken and returned, since from now on he must watch over that sheep and ensure it does not behave abnormally compared to how it was before. Therefore, there is an obligation to inform him that it was stolen and returned, and thus the thief will exempt himself from any further responsibility for whatever might happen to that sheep. This is the essence of the Mishnah.
The text of the Mishnah:
"Hagonev taleh min ha'eder vehachziro" - One who steals a lamb from the flock and returns it to its place, and this refers to a case where the owner did not know either of its theft or its return. Since we are concerned that the lamb might change its behavior from how it was, and the owner does not know to pay attention to this - "umeis o nignav", if something happened to that lamb, that it died or was stolen or any other incident - "chayav beacharayuso". The thief remains responsible, and he must pay the victim a new lamb, since the owner did not know to change his behavior, and it turns out that the thief did not exempt himself from his obligations.
"Lo yade'u be'alim lo begenavaso velo bachazaraso" - this is the condition under which the law is stated: that the owner did not know about the theft nor about the return.
However, if the owners knew about the theft, and they seek to find out what happened - "u'manu es hatzon ushleimah hi" - they counted the flock and found it complete, and said: The sheep that was missing has returned to the flock - "patur" - he is exempt. As long as the thief knows that the owners know the sheep was returned, he is exempt from further responsibility, because the owner says to himself: Apparently the thieves returned it, and from now on we must keep an eye on it. Even if he knows there were thieves here, he says: It has returned to its place, and we will probably have to guard it better in the future.
In summary: We learned that returning stolen property without the owners' knowledge depends on whether the owners knew about the theft. With an inanimate object - if they did not know at all, their guarding continues as usual and the robber is exempt; and if they knew about the theft but not about the return, the responsibility remains on him. With an animal, however, since its departure from the owners' domain may alter its behavior, returning it alone is not enough, and the thief must inform the owners about the theft and the return in order to be exempt from his responsibility.