Some addendum to this. Hendrix' order denying the TRO in Texas. https://www.courtlistener.com/docket/69898198/27/aarp-v-trump/
"But the government’s response confirms that it has no present plans to remove either petitioner until the habeas petition is resolved and that it will notify the Court if that changes. Dkt. No. 19 at 12–13. The government once again confirmed its continued belief that “the requirement for judicial review includes a process for affording notice and opportunity to be heard prior to being removed under AEA authority” and that once “that opportunity to be heard has been satisfied, removal may proceed unless a court orders otherwise.” Id. at 13. The government further provided a declaration from Yousef Khan, Assistant Field Office Director for the United States Department of Homeland Security, Immigration and Customs Enforcement, who stated that “ICE does not intend to remove A.A.R.P. or W.M.M. under the AEA while their habeas petitions are pending.”"
That seems to be some pretty affirmative shit from the government. Almost acting lawful.
HOWEVER, what it says is that the two named plaintiffs will not be deported, but the petition represents a class of persons, namely those held in ND Tex pending deportation. Gubmint doesn't say a thing about them. Also, it says "under AEA," which leaves some wiggle room for removal/deportation under some other bullshit.
Of course, one response to this by the court would be to actually enjoin them from doing what they say they won't do, along with the other putative class members. Bit hard to argue with that or appeal.