When I was living in EY for the first few years of my marriage we rented an apartment from someone who was not "chareidi" who inherited the apartment from his mother whose background we had no knowledge of at all. In the storage area in the ceiling above the hallway were some rolls of schach that I could not find out anything about and the landlord had no information about the source either. I saw R Dovid Mor who has a reputation as a machmir, and asked him about it and his reply was "What could be the problem with them?"
