I dont understand all the resistance to providing proof of residency. Cops ask for ID all the time, which translates to "your paperwork". They need to know who theyre facing. I imagine it could be abused, but the average cop just wants proof that you are who you say you are. Whats wrong with that.
Being here illegally is AGAINST THE LAW, last time I checked.
And if you dont wnat a cop to have the right to ask you to prove exactly who you are when they stop you for a legitimate reason, and you are here illegally, then you should return to your country, where I'm sure you will have all kinds of better rights.