I used to volunteer in a hospice and it shocked me that some of the people had family who would just never bother to visit.
She could have another 20 years left in reality and if she is all there I can't see the prospect of being in a home being particularly welcome to her, especially the state of some of them.
My great nan was still very active well into her nineties, we would often go round to find her doings bits in the garden and all sorts. I think her finally going into a home was what made her give up in the end. Even then though she used to escape and they'd find her a few miles away, often up a hill, having just fancied going for a walk :)
I have to say, the one my nan was in when she developed dementia then had a fall and developed MRSA in hospital was fantastic (my uncle lived with her until then). She died there with a lot of the family having been round her bedside constantly and a number of us being with her when she finally passed away. She had developed pnumonia and sceptacemia and wasn't conscious at the end but her room, bedding and even herself was always spotlessly clean and very well cared for and the staff were fantastic especially as there were so many of us.
I think the spare key idea is a great one. A few weeks ago I noticed some police cars and an ambulance outside my nextdoor neighbour but one's house. The poor guy had died and been there up to two weeks. He kept himself to himself but a lady from his church called the police when she hadn't seen him and they came and broke into the house and found him, so very very sad.
A local volunteer bureau may also be able to help. One I was a part of used to find people to help with things like shopping and company.