I can see that, but wouldn't he have mentioned this to her by now, if he had been expecting it a while? Why wait until he signed up with a real-estate agent and was looking at houses and she called him on that? It doesn't sound like he was trying to surprise her (or he would have said so).
Inheritance doesn't necessarily happen like that. My grandmother died when I was 17 but I wasn't entitled to my inheritance until I was 21 as that is what was stated in her will.
He might not be correct about getting an inheritance next year. Inheritance does not usually take a year; someone dies, and the estate gets probated, and that is it. So many people have gotten into financial trouble when they count on getting money when someone dies -- people leave their money to charities, to friends, not necessarily to the person next in the family lineup.
So, don't worry about the issue of whether or not he will report the inheritance to the state, yet. If such an inheritance ever really comes, then seek some legal advice. You could even call the assistance office from a pay phone and not give your name, and ask them directly.
Regarding getting a loan on a house, be sure you are not on the paperwork if you think there is any chance this will be defaulted. If you are seriously worried that doing this will run both of you into bankruptcy, that is actually a pretty good reason to get a divorce, so you won't be obliged to cover the house payment simply by virtue of you having been married to him when he incurred the debt.
Frankly, the inheritance story sounds pretty fishy to me, he probably just invented it or embroidered a possibility, to get you off his back. The fact that he came flashing back after telling it and you poked holes in it, is more characteristic of someone acting defensive about a tale that is full of wishful thinking than it is of someone who is really sure it is true.
I'm sorry you are feeling so poorly, and hope that you two can come to some kind of understanding.
I wouldn't risk it. There's consequences, either repaying back, or jail time.
You will not be able to accept the money without the government finding out somehow.