I refused to sign anything, they billed it to DHS, DHS refused it and put that I was the responsible party, then the hospital sold it to debt collectors under my name.

Granted I've never seen something like this where the chain includes a government agency saying "it's totally on this guy", but normally you can get good results from writing a dispute letter to the debt collection agency telling them to prove that you really owe this debt. The state of the industry normally means that they will not have gotten anything like actual proof from the hospital, just a line item in a spreadsheet... and if they can't prove it they're legally barred from contacting you about it or reporting it to credit bureaus.

(I've never done it, but I suspect you could get rid of a significant percentage of real debts like this, just on the strength of the industry's terrible record keeping practices.)

Yeah done that many times. They always just send the "spreadsheet" entry as their proofs. Sometimes they stop despite their "proofs" and just sell it to the next debt collector and everything resets. Other times they just keep doing it and then I get the CFPB involved and after a few months the regulators stop them, then they sell the debt and the new guy pursues it again.

Just something I deal with every year or two, doing the process over again every time they resell it.