There are two scenarious where they would: one, of course, if both parties reach some written agreement regarding it you can divide all or part of the equity and write in all kinds of conditions and possiblities etc..

two, you could file a motion with substantial supporting evidence showing why you absolutely had to have a portion of the equity now.  the court could do it, you would have to make that motion to the assigned judge by the way not on the motions calendar, but usually they don't make divisions like that until trial.  if you had to have a certain kind of surgery they might do it.