held in the nation until convicted. Im calling that "letting them stay".
Unfortunately, they have a right to their day in court. Until then, they are flight risks and should be, to the maximum extent possible, paying their own way while incarcerated awaiting trial. If they don't like that, they can always sign a guilty plea and be immediately deported.
My preferred method would be the court requires verifiable proof of citizenship from their country of origin. We won't take their word for it. Upon being convicted of being in the US illegally, they are then randomly deported to a nation of our choice halfway around the planet where they are summarily dumped off to fend for themselves.
"Bailiff! Spin the Wheel of Deportation!"
'Budda, budda, budda.... The wheel stops.
The judge looks at the wheel, "Uzbekistan! You're from Uzbekistan! Officers, deport him to his country of origin..."
"But senior judge, I am from Honduras!"
"Not according to our expert opinion since you have no records to prove otherwise..."
Bet it wouldn't take long for every illegal in the US to start fleeing the country and nobody wanting to come if we did that...