I appreciate everyone's thoughts. I confirmed with the husband's nursing home that he is basically in a non-communicative state, and will never live on his own. I am not even sure he is aware his wife passed away. I consulted a local real estate attorney who specializes in tenant-landlord affairs. In my state we have to provide a 30 day move out notice. Legally I have to mail that to the last known address. At the end of 30 days, if I the belongings are moved out to my satisfaction, I can proceed to ready the house for new tenants, including disposing of the belongings. The state sees it as he is voluntarily leaving his belongings behind. If I am not satisfied he is out, I can file for eviction. But that takes months, and is a lot more hassle. He did suggest I communicate with the only known relative about the contents of the home, and give them the 30 day notice as well, which I have done. So the game plan is after 30 days, I just dispose of the contents, whether I sell, donate or junk. If there is anything I can sell, it will go toward recouping some of my costs. In the meantime, I am already in there starting on some of renovations, cleaning out old food, changing utilities to me, etc.
Again, I can't reiterate enough how sad of a situation this was. Make sure you have your end of life affairs in order.