broken skirts result in a few things.....
* the simplest is the skirt gets caught before it enters the bottom end and locks up the rod/crank
(if the full piece is found, you may gamble)
* the broken piece being chewed up into a million tiny pieces by the rotating crank (miss even one small piece and it may wipe out your main/rod bearings and the new top end = more $)
* it enters the bottom end and pieces are forced thru the cases into the counter balancer or transmission areas
creating a huge air leak (which will also quickly ruin a new top end = $$$)
since you didn't find the broken piece, chances are very good it got chewed up by the crank, you need to split the cases to clean out any and all remaining pieces, inspect the rod bearing, and for case damage/cracks, and while your in there replace the main bearings and seals.
unless you win the lottery weekly, don't gamble with this, you will lose.