Suppose a non-observant Jew dies while possessing items forbidden to own. I was taught recently in a class that inheritance, unlike other transfers of property, happens immediately and automatically; no kinyan is required. If he has Jewish heirs, therefore, they come to automatically own the forbidden items, whether they want them or not. What should an heir do to minimize further transgression? May he sell or give away the items to a non-Jew (to avoid waste in the case of food), or does he need to destroy them? Must he do so immediately, or do we say that once he's the owner of forbidden items anyway, there is no further damage if he still owns them tomorrow?
One example of forbidden ownership is chameitz during Pesach, but it appears we do not need to be concerned about this case because the original owner ceased to own it when Pesach started, per Pesachim 6b (h/t DoubleAA), so it probably can't be inherited. Other examples would be items used for idolatry and untithed fruit. Some comments suggest following the example of the mishnayot in Demai chapter 6, and I'd welcome an answer that explains how to do that (and supports it as an appropriate precedent). Another comment questions whether such items could be owned (and thus inherited) at all, since they have no value to a Jew, so perhaps there is an argument to be made along those lines.
This question was prompted by this question about a convert inheriting from a non-Jew, but it sounds like both the heir being a convert and the other being a gentile are relevant to that case. I'm asking about cases involving only Jews.
