If you're a foreigner living abroad, you'd best be prepared to prove you have the legal right to be there at any time.
With the prevalence of the ACLU, and all the other screaming-meemie Meatheads, there is no way that people would not be given a reasonable chance to prove residence. A 30-day trial waiting period is unnecessary. We're just talking about deportation. In the extremely unlikely instance that someone were actually wrongly deported, I'm sure the Mexican (or whatever foreign) government would help them in any way necessary to get back.
HB 4437 is a well thought-out piece of legislation that will have exactly, precisely, the intended effect: slowing or halting illegal immigration. Thus the reason its' detractors are so rabid in denouncing it... ...it would actually work, so they're doing everything in their power to stop it.