As a bit of thread creep, would it be possible to fly on just the elevator trim or rudder trim if the primary cables / rods failed? The PA28 has a paticularly large trim tab. I know i'd certainly give it a go if it happened.
Happened to me once, left rudder cable broke
. Takes a few seconds for it to sink in, but when it does it's quite a simple fix, albeit a temporary one.
Whichever side goes u/s just wind on FULL TRIM in that direction (ie: left goes, full left trim, right goes, full right trim) AND, this is most important, LEAVE IT THERE. You can gain enough control back with the opposite pedal alone to get you on the ground safely.
Same can be done with a broken aileron cable, although perhaps not so effectively if you don't have aileron trim, and with the elevator (ie: UP elevator breaks, wind on nose up trim and balance with forward pressure on the control column. Next time you go flying, try it with the rudder (safely of course!) and see how it feels. It takes a bit of getting used to but it could save your life.
Stay safe
AS