Hi Dansemacabre1971, welcome to the group

You're definitely with people who are working through similar questions as yours:
I've called his sister, friends and the crisis line for advice. No real help there. I've sent periodic reminders that he can come eat and that I'm open to talk.But mostly just respected his wishes and left him alone.
What can I do? What should I do? Is this emotional terrorism or a cry for help?
I'm curious, how would you have approached this in the past? Do you tend towards feeling that it's your job to help him?
BPD has many facets. One that comes to mind here is that pwBPD often use low-skill or immature approaches to try to get needs met, as their needs (especially emotional needs) often seem to be unending and unfulfillable.
One way to look at this situation is that a mature person might say with words "You know, I'm having a hard time, and I'm going to take some space for myself. It's nothing to do with you, I'm just going to spend time alone to get grounded again. I'll text you in the evenings to let you know how I'm doing." I.e., the mature person can get needs met by self soothing.
Your partner doesn't seem to have that kind of skill level. Perhaps he is trying to communicate the same thing, and the way he is doing it is by pouting, sulking, huffing off, silent treatment, "I can do what I want, you can't make me", and passive bids for others to take responsibility for him. He doesn't have mature skills and may want others to soothe his feelings, and also can't communicate very directly.
Just some impressions.
So, if that's the case, I think you're on the right track to "believe what he is communicating", leave him alone, and not try to solve his problems for him.
As he is an adult, it's unlikely he will starve to death, or forget that he can talk through things. What if you gave yourself a break from doing those things for him, and focused on how the kids (and you) were doing? He may be on his own timeline, versus anyone else's, for "snapping out of it" and in a weird way, "believing what he's telling you" that he doesn't want to interact, can help him self soothe and learn to manage himself.
...
The drinking is an issue, and lots of members here have partners where alcohol is a major issue.
Have you checked out any Alanon type groups yet?
Lots to talk about re: alcohol, but we can start there.
Keep us posted with how the last few days have been for you, whenever works for you;
kells76