How do I collect from a dead beat Ex-husband since he is on Public assistance and DSHS Child support can't touch him?

As long as he's on public assistance, you're not going to get any support from him, unfortunately. It's not clear what kind of public assistance he's on. If it's disability-related, ask at your local CSO if there's an additional benefit you can get for the child. If it's income-related, provide the CSO with a copy of your child support documents and a letter from you for his file. That way, if/when he comes up for eligibility review, DSHS may have greater expectations about him getting off his bum and getting to work.

Also, if your order of child support allows him to claim any of the kids on his taxes, ask the court to change that provision. That's an easy do-it-yourself motion. At least you will have the maximum tax benefit.

how old are the kids? The statute of limitations for collecting child support runs out 10 years after the youngest child turns 18. You can ask the court to extend the statute of limitations. I was the lead public defense attorney on child support in my county for 6 years and never once saw a court deny that kind of motion. Once it's extended, you have forever to collect support.