I'm just anticipating all the things that are going to make the divorce step challenging, and I think this behavior, oddly enough, makes me feel worse than a full on argument with yelling.
My ex did this. I would try to repair or recover from something, or try to get a conversation going about something, and he would go total radio silence. Sometimes a dead stare dripping with contempt.
In Patricia Evan's book Verbal Abuse she talks about how the silent treatment is the worst form of verbal abuse because it makes you feel erased. It is the cruelest form of invalidation, you aren't even worth talking to.
I didn't discover a lot of this until I was out of the relationship, but I have a colleague who does a version of this and what I do is fill the silence so there's no erasing happening and there is no satisfaction gained because I am not suffering (to send the signal that silent treatment isn't a behavior that's effective with me).
It doesn't make the situation easier necessarily, since silent treatment can be aggressive behavior, not to mention awkward. It's more about removing payoff for bad behavior.
I guess the other piece here is how you tell him in a way where you're taking care of yourself.
Just brainstorming aloud here, thinking about the ways BPD and codependent dynamics tend to play out. How about something like:
"This isn't working. I'm learning that I'm not cut out for caretaking. It's what I did as a kid, and I've done it with you, and the next chapter in my life is about figuring out who I am when I'm not taking care of people. This is probably a lot to drop and I know it's going to take time to process -- I can give you lots of space to work through this, I know you like to reflect in quiet. My things are packed and I'll be staying at xyz. Reach out to me when you feel ready and we can talk about next steps. You have this great therapist, it's best to reach out to her/him if you need emotional support because I'm pretty overwhelmed myself and can't provide a whole lot of caretaking, since I need a lot myself right now. You know how to reach me when you're ready to talk about where we go from here."
Something like that, but in your words?
I highly recommend having a refrain you can keep returning to, something like, "I am not cut out for caretaking." "I am really not cut out for caretaking." "I am really, really not cut out for caretaking."
It's about you, it's your truth, it's expressing your limits, it was true in the relationship and it will be true during the divorce. You can be kind, compassionate, a good listener, a caring, good person. And you can recognize you are not going to be a caretaker any longer.
Tried it, didn't like it, didn't really work.
He's probably not going to say, Yeah -- you're right. It's not fair. I'm a full-grown man-child with serious addictions. I need to work on my stuff and get this depression under control because we both know this is my burden to carry. I'm not ready for a fully committed relationship because this other stuff is crippling our relationship and making it impossible to reciprocate except in short bursts that I can't sustain.
He's probably going to FOG you. "How could you do this to me after everything we've been through, I went to therapy for you, I haven't had a drink in 6 hours and quit smoking pot for 6 whole weeks." Or?
If he goes silent, I would have a plan to get yourself to a place where you'll feel supported, like talking to a therapist, your friends, or something you do when you need to get centered. Be intentional like you would be if this were your younger sister, 10 years your junior. What would you suggest she do?