I don't know if this is likely, but perhaps Paxton would accept a contract like that based on the fact the SOX were paying him for quite a while when he wasn't able to pitch. But, cynical me believes he'll go to whomever pays him the most.
The SOX are much better off than the Yankems. They can't win much w/o their best player. The SOX, otoh, would be much more competitive offensively if they were to lose their best offensive player. IOW, W/O Judge, the Yankems' offense sucks!