I think the process is different for asylum. Asylum is when you are facing persecution or harm. You can be allowed to stay in the country while the government makes their decision. If it's granted you get residence for your family, if it's not you get kicked out.

This is about the government making arbitrary decisions about who gets to stay (illegals from mexico) and who needs to go (europeans). It's not a matter of them not paying fees to stay in the country.