Well here is what I think but please forgive I am a newbie. First thing that comes to mind is talk to a lawyer to find out rights for you and her. That being said I mean what is the holding period on your behalf so if she is on a lease and passes how long can you hold her stuff in a storage unit locked before you half to trash it or send to next of kin.
Next thing if she is on a month to month there probably is no holding period and its up to you on what to do next. I would go above and beyond in this situation. I would check on her in the hospital if she is definitely not coming back I would try to talk to her relative see if she wants to stay in her place to make sure her stuff is kept safe. That will get them thinking oh I need to figure out what am I going to do with her stuff it is also going to look good on you.
You want to look sympathetic but not week so if she pulls through she will know you were there for her at a stand point. And here relative will know that you will be there but you also have a business to run. We are all human and we all need someone to watch out for us. But most important CYA for you (cover your ***) talk to a lawyer find out laws for situations in this. Does she have a will is he a donor does she have a church etc. A lot of people that I know that have passed leave their stuff to friends and churches. I hope this helps. Jon.