In a Becker-Posner blog, Gary Becker objected to amnesty and instead proposed that illegal immigrants should be allowed to buy their legality by paying say a $10,000 fine. This is trumpeted as the Chicago principle of markets as the answer to many problems.
Instead of asking illegal immigrants to buy the right to stay, why not ask their employers to buy the right to keep them in the country? Doing so could free employers from any legal action against them for employing illegals.
Markets are wonderful, but the question is always who is the buyer and who the seller.