I doubt it. The thieves would first have to go thru an immigration court to be charged with violating immigration laws, then local and/or federal courts could charge them with the various crimes committed which violate either or both jurisdiction’s laws. All during this process their lawyers funded partially by the taxpayers or groups such as the ACLU will be filing appeal after appeal to get their release back into the general population on humanitarian grounds & other dubious, irrational legal claims. BTW, their is a backlog of 600,000 cases in the immigration courts, so it might be some time before individual cases are heard. For those who conspired to commit mass identity fraud or have other felony convictions an expedited method can be used to get them thru the courts, but if that is true why did they not go thru that same process the first time they were detained for a criminal act. Answer, in many cases the local arresting authority does not report the incident of crime to ICE and/or ICE does not have sufficient manpower to cover all the volume of violations. In addition, sanctuary localities do not even attempt much of the time to report such crimes to ICE, unless they have to do with more serious crimes such as drug smuggling in which case FBI normally takes jurisdiction.
BTW, here is a list of sanctuary cities for the USA. http://ojjpac.org/sanctuary.asp
You can sue a thief, a trespasser, a batterer or assault-er--it's what they did to OJ after the criminal courts failed. It's called an "intentional tort". Check your homeowner's policy--you're not insured for an intentional tort. You can't punch a guest in the nose and expect your insurance to cover you.
And there's such a thing as being complicit in an intentional tort--like aiding a dangerous trespasser, helping (or seeming to help) someone to get false ID--
I've wondered if ranchers on the border could go after those who help illegals trespass and trash up their property...like these do-goody church leaders.