I'm not a lawyer, but years ago I read a book on contract law that one of my tenants had thrown out. I just finished re-reading the section called "adverse possession", and that's what this squatter woman's lawyer is probably going to argue.
Canada and the USA both inherited their system of laws from England where 500 or 600 years ago only the very wealthy and the clergy could afford time away from work to learn to read and write, and the Lord who looked after the land on behalf of the King would often be gone for years fighting a crusade somewhere in the middle east. So, back then, it was common for people to try to swindle people out of their property by bribing someone who knew how to write to forge a will or deed. Then, they'd make up a story as to why they had a superior right to that land. Illegitimate children of deceased Lords were popping up all over the place back then. With no Lord around to decide the matter, the principle of "adverse possession" became part of the "common law", which was really just the rules of common sense that people lived by under those circumstances.
Adverse possession simply means that if you occupy someone else's land openly and treat it as your own by farming it or making improvements to it, and you do that for a long enough period of time, that land becomes yours.
So, if you're an illiterate farmer in medieval England, and some stranger shows up on your doorstep claiming that he's the rightful owner of your land and has a piece of parchment to prove it, you didn't have to worry because all of your neighbors would testify that it was you who had farmed that land for years and you were the one who built the barn and thatched the roof on it and built a fine pig sty for your sow too. In that case, the principle of adverse possession would come into play, and you would succeed in keeping the land despite the apparantly superior claim of the stranger.
I'm not a lawyer, but there's no chance that this squatting Blair woman is going to get herself a free house here. When Peterson bought the house, then she would have been recorded as the owner in Detroit City's property tax department. Lots of cities have programs whereby if someone fixes up an abandoned derilict house, they become the owners of it, but all of that has to be done with both the registered owner's and the city's knowledge and permission. If this ever gets to court, the judge is gonna see it for what it is; a modern day attempt to swindle someone out of their property.