Wow. I am so sorry about this for you and your children. I cannot believe anyone would do this. He sure sounds like he is making some major plans or already has. You are asking if he can do this. Well I hate to say it but he probably can, legally. However, legally, you can also require him to give you money. Sounds like you guys arranged your financial affairs after the divorce on your own and it worked out for you. My wife and I when we split did the same thing. However, it might be time to revisit the court system and require a monthly payment from him if he is going to just give up and leave you all to pick up the pieces.
I am in no way qualified to really offer any advice on what he might be thinking or anything. But I do know that it sounds like he shouldn't be able to just walk away like that without haveing to share in at lease the financial responsibility of your children.