Abandoned 45 years ago-still married?

My MIL's husband left over 45 yrs. ago. He is an alcoholic on the streets. We saw him several years ago, so we know he is still alive, but that's about it. He never gave her a cent or saw the kids. My DH, my MIL and I bought a home together 10 yrs. ago and has always filled everything out as "a single woman', so it says hers and our names on the house deed.

She could never afford a divorce, so just ignored it, but now we are thinking (a bit late, I know) if he or anyone he owes money to, would have any entitlement to our house when my MIL passes away. Any suggestion?

Also, is it possible to get an inexpensive divorce when there is this kind of desertion, or is there a common law divorce type thing? We live in California.

Thanks,
Kip