i think leaving to live with his parents for a monnth might have driven those nails into this coffin. She was feeling abandoned, and formed a plan forward without him.
A separation...does not seem like a useful thing to me unless you are pretty sure you DO want the relationship to end.
I don't think it was such a bad idea for him to get out of a toxic environment, TBH. When my ex wife decided she was leaving, it took her a week to actually do so, at my insistence (and with help from her sister). Not everybody is so lucky that the other person will actually leave. If you're at an impasse with this sort of thing, then it's not the worst thing in the world for you to leave the home. It's not ideal, but in the grand scheme of things, actually being separated from the person is a positive. Preferably it's them that should leave, but it doesn't always work out that way.
IME, the only tiny sliver of hope for me would have been to do the 180 - something I didn't know about way back then. People are funny that way - when they reject you, they EXPECT you to be upset and beg and cry. They actually prepare themselves for that. When you don't react in that way, THEY are the ones who sometimes end up feeling rejected and it makes them start thinking about things in a different way.
That kind of thing might only work if you aren't an a-hole or ever gave them a legitimate reason for them to leave you. In my case, I was a pretty good partner and husband.
Chasing someone who doesn't want to be with you actually drives them further away - I know that now. They're expecting it, and it's often a point of pride for them to 'stand their ground' with their decision. They're prepared for the waterworks and the 20-questions and the over all sadness.
It's damn-near impossible, but ideally, one should just live their life and go on when presented with something like this, as opposed to stopping everything and making the other person the center of their universe.
I started dating about 3-4 months after my ex wife left, and she found out shortly after. I didn't make a big deal of it, or even tell her, she found out on her own. And her tune changed drastically towards me, almost like jealousy. In retrospect, it was kind of funny. I took steps to move on from her, and it was almost like "wait, you're not chasing me any more?" At that point, she had rented her own place, all our pets were still living with me, and the man she left me for didn't live in this country and she was a few months away from moving there still. So I started dating someone, was living in 'our' house with all our pets, and she was all alone.
The sooner one can do something like that (not necessarily date, of course, just be 'okay' with the situation), the better. Especially if the other person has narcissistic tendencies, like my ex wife did. When you don't act in the expected way to rejection, it throws them for a loop. But you also can't force it and make it obvious. They're not going to be jealous if you suddenly turn into a party-boy/girl or turn to booze or otherwise go off the rails. But if you just live your life normally and be happy, that's another story. People are funny like that, like I said.