I missed that bit about the 14th amendment.
This has nothing to do with the 14th amendment. The 14th amendment argument is about who gets ius soli citizenship (what they call "birthright citizenship"), not about the treatment of anybody who's agreed not to be a citizen. The administration has made claims about jurisdiction limiting what they have to do for non-citizens, but not on that basis.
So far I don't think they've actually tried to deport anybody born on US soil. If they do, then the 14th Amendment comes into play.
The existing cases are about the 5th amendment, Article 1 habeas corpus, common law, immigration statutes, etc, not the 14th.