NO. NO NO NO. Round ‘em up, throw ‘em out.
No need to round 'em up.
1) No work without citizenship/legal status.
2) No government benefits without citizenship/legal status.
3) No deportation-proofing of entire families for having anchor babies. (Anchor babies get deported along with their families but can return at age 18 if they choose to do so. Canada does this and it makes sense to me.)