Unfortunately immigration is within the Federal domain and the states, no matter how loud they scream, can do nothing to prevent ‘refugees’ from being settled within their borders.....unless they threaten and are willing to utilize succession.
There is also the constitutional provision that they may act on their own to repel invasion.
Might not be able to do this with formal beneficiaries of the refugee program. But a quid pro quo with illegales might be quite interesting.