I’m not sure I know what you are saying. Obviously, if the natural mother wants to be cooperative, she can help identify the father. But what can she be forced to do? Name names? And what if she names 100 names, and 100 DNA tests come back negative?
That is how it works and yes they will test all and keep testing. I know a guy who had to go and do this once with a women. He was mortified to find out there were 13 other guys waiting to be tested for the same thing for her.