In fact, borderline human rights compromise is actually a good incentive for people to leave. Would perhaps be good for the country if those in Texas who respect human rights would move from Texas to Pennsylvania for a human rights upgrade (where also the death penalty was repealed).
But I doubt your statement is accurate considering inbound refugees are fleeing from even worse conditions w.r.t. human rights. Refugees still technically have their human right to access emergency medical treatment, they just risk getting harassed and tagged for deportation.
Asylum is a legal process. If they follow that process (which begins with claiming asylum), then of course they cease to be illegal immigrants throughout the process.