No, just deported. When the Navy shoots at Somali pirates they don't worry about jurisdiction. The left has been at pains to point out that illegal entry is not a crime and border patrol is not law enforcement, but that cuts both ways.

> You think if they do some big crime the US is going to ignore it and do nothing but give a referral because oops no jurisdiction?

If they do a medium-sized crime the US ignores it and just deports them, that much happens all the time already, no-one wants more people in prison.

If they do a big enough crime then I'm sure the US would find some way to charge them, but that's no different from what they do for full-on foreigners who never come anywhere near the US. E.g. if they kill a US citizen on US soil then the US would claim jurisdiction on that basis, even if the perpetrator stayed on the other side of the border the whole time.

If you were being reasonable, you might realize that short of those crimes deserving the death penalty, our country is better off just deporting. I don't want to spend $50,000/year (and up) on sequestering someone from our population, when deportation accomplishes that same result. Just make sure the deportation is successful. Send them with a crate of evidence for local prosecutors (who, in theory, should want to prosecute them... unless they really were sending them here to destablize our country with sabotage and rape).

This would remain true for me, even if it had no impact on citizenship of their children.

And I could imagine situations where it makes sense to prosecute and then deport with a suspended sentence, which keeps costs relatively low but also gives them a much bigger incentive to never come back.