Whenever I've been in the stack I've had the impression that the lowest aircraft gets pulled off first and then everyone else gets to step down (1000 ft?). If the stack gets more than 3 or 4 in it it must be a nightmare for the controller to take the bottom one off, tell the one above to descend 1000ft, wait until that has at least started (or wait until it arrives at the new altitude?) then move the next one etc all the time managing the ones that have already started their approach and bringing in new aircraft arriving at the top of the stack.
Does the situation ever arise when you need to take one out of the stack out of turn? I guess you simply assign a heading out of the stack and then descend it a bit quicker than normal to get it into the line for landing. Then you just reassign the stack above the removed aircraft.