Actually, my proposal was more institutional... But your idea of some sort of bounty on illegals is worth further consideration. Especially since the illegals would be paying it themselves.
One problem would be to build in safeguards against overzealous agents.
I saw that, and I couldn't help myself, I tweaked it a bit. I agree that overzealous abuse is probably certain in the long run, and a mechanism would be needed to deal with it. More immediate is my belief that a great many INS and Border Patrol line agents are NOT corrupt and want to do a good job and obey the Constitution while enforcing the law with vigor, but they are hobbled by politically motivated superiors. A bounty situation might get this moving.
It is interesting to note that RICO statutes contain effectively a court approved bounty for civillians to collect, as does much enviromental legislation.