In situations like this, both parents need to find outlets to process their anger, upset, guilt etc in ways that don't involve the children.
All of us benefit from having 2 loving parents. Sadly, this isn't always possible due to death or lack of capacity to parent properly. In the latter case, the ideal situation is for the parent(s) who are incapable to parent well, or even satisfactorily, to get better at it.
It would be best for your children if you could work out how to support him being in their lives- not for his sake, but for them.
-If he is genuinely a danger, the risks need to be addressed before he sees them alone.
- If they aren't used to being alone with him, without you around, start off slow- with short contact (he could do school drop off or pick up, or taking to a club/regular evening activity). Once they experience him as being someone who does things with/for them, visits and time together will feel more natural.
- If they find being with him awkward, suggest activities they can do together that will interest the children, so their focus is on the activities rather than him. This will help grow their relationship.
It's really hard to step away from thinking about his relationship with the children in term of whether he 'deserves them'. Try and think about what they deserve in terms of a relationship with the only father they have. They may deserve a much better father than him, but that's not what they've got.
If you think he is unsafe for them to be around, then you need to take action to limit his rights. If you thought he was safe to be alone with them a month ago, before he walked out, think what is different now.
Him choosing not to live together anymore and opting out of taking responsibility for his children's everyday needs is total fuckwittery and totally shit on many levels. I would be incandescent with rage and resentment. I expect I would want you to deny him every benefit from having the children in his life due to him walking away from every demand that comes with having them. BUT, in wanting my children to have the best life possible, I know that I could let this play out by ruining their chances of having their dad in their lives.
You can have boundaries and don't need to run around in rings to facilitate a relationship ship between them. Try and think about what's going to be easiest for you.