The gemara says that in the days of rebbi they made a takanas hashavim that if one stole or took money as interest, he does not have to pay it back (the beis din is not even allowed to allow the nigzal to receive it), so that people will not be discouraged from doing teshuva. The gemara limits this to gezeila that is no longer here to return, but when the object is here he must return it. Tosafos continues to limit this takana even more by saying one of the following: a. it only applied during the time period of rebbi, not before or after. b. it only applies to a professional thief who would more easily be discouraged from teshuva. c. it only applies when he is coming forward to repent, not when he is caught and forced to return (tosafos rejects this approach).
However, the gemara mentions a more mild takanas hashavim that is paskened in the poskim. When one steals a beam and builds it in his house, technically he should be required to break down the entire structure to return the beam. However, chazal made a takanas hashavim to allow him to return the cash value of the beam rather than the actual beam (rashi explains that the takana of rebbi doesn't cover this case since the beam is still here and can be returned, that is why this takana doesn't exempt the thief completely).
In Shulchan Aruch (c.m. 360) we pasken that the beam doesn't have to be returned and it is sufficient to return money. However, the rama writes that if one were to steal property and construct a house on that property, we would not make a takanas hashavim allowing him to pay the cash value of the property. When it comes to theft of property there was not takanas hashavim. Why?
The sm"a (360:6) writes: דלא עשו תקנת השבים בקרקע דכיון דהוא דבר קבוע ועומד הו"ל למידע דשל הנגזל הוא ולא הו"ל לקנותו
This implies that the takanas hashavim was really only for one who purchases stolen goods without realizing that they were stolen. This would not apply to property since everyone knows to who it belongs. The approach of the sm"a is a big chiddush because we never find that the takanas hashavim is limited to one who used stolen goods accidentally. The be'er heitev writes over the sm"a and replaces the word "לקנותו" with the word לבנותו (nesivos also makes this correction), but the magiah on the be'er heitev is still not sure what that really accomplishes.
The Taz seems to understand that the takanas hashavim was not only for the benefit of the gazlan to do teshuva but also for the nigzal. It is very likely that without the takana, the stolen item will never be returned and will eventually rot away. They made it easier for the thief to do teshuva to protect the nigzal and make sure that he is reimbursed. Property which will never disappear, and eventually be returned to the rightful owner when Hashem decides to weaken the hand of the thief, they didn't need a takana to protect the nigzal. The Pischei Teshuva quotes the levush who has a similar approach, that property which cannot be hidden and will eventually be returned, does not require a takana to protect the nigzal. The difficulty with this approach is that the takanas hashavim of rebbi was purely for the benefit of the gazlan to encourage him to do teshuva without any concern for the nigzal. Presumably, this lower level takana which makes the gazlan at least return cash, is also for the benefit of the gazlan, but not instituted to benefit the nigzal, therefore it should apply to property as well.
A completely seperate issue - R' Akiva Eiger refers to the chavos yair who discusses a situation of a goy who steals from a jew and then converts, must he return stolen goods that he has. He quotes Tosafos in sanhedrin 71a who asks why a goy who commits murder and then converts is still chayev misah, we should say that he is כקטן שנולד דמי, an entirely new person? Tosafos answers that b'dinei shamayim he is like a new person with a clean slate, but in dinei adam he remains responsible for the acts he commited as a goy. Therefore, he is obligated to return an item that he stole as a goy. Basically, the idea of גר שנתגייר כקטן שנולד דמי, is the equivalent of a jew doing teshuva, but that will not remove from his punishments from beis din or returning stolen goods. But, the question can still be asked whether there is a takanas hashavim for such a situation - For example, a goy stole a beam and built a house, he then converted, would there be a takanas hashavim to allow him to pay cash rather than knock down the house?