I can solve this instantly.
Pass a law mandating a $1,000,000 cash payment to any person mistakenly deported, for each 30 day block of time they are not on U.S. soil. Day 1-30 is $1,000,000, $2,000,000 for day 30-60, and so on.
If the person cannot be located within 12 months or is killed before they can be repatriated, the $12,000,000 goes to their survivors, doubled if there is evidence of a wrongful death.
They'll start triple-checking their work in a *big* damned hurry.