Simple. Turn them over to ICE.
There's the problem. Bush and the GOP congress doubled the number of Border Patrol agents but hired no new ICE agents. After the meltdown in 08, none have been hired.
Back then, local govts & local law enforcement were asking for more ICE agents and that is actually why the number of Sanctuary Cities exploded during the Bush years.
If ICE wants these people they need to send somebody to pick them up, right away, instead pushing the cost off on the local taxpayers and forcing local law enforcement to illegally detain these prisoners.
This is like many problems, it could be solved by spending more money. The GOP congress need to appropriate more money for more ICE agents, court rooms, judges, jail cells, etc.