IMO they will do what they always do, when popular opinion shifts they will simply shift with it and deny every being on the other side or justify it somehow coinciding with more evidence or proof or studies or whatever coming out around the same time as the public opinion shift. You never knew better than them and the vast majority will sheep right into the new reality without actually waking up. Just my opinion tho, try to have more faith in humanity than I do, I can be pretty miserable.
Those whose home countries will not take them back get free helicopter rides.