How to arrest Cat6 cables from falling inside the wall?
Purchase ring-ended cable ties.
Put a short drywall screw (or other wood screw, assuming wooden studs) through the ring.
Reach in the hole and screw it to the stud that's closest.
Grab the cables and thread the cable tie around them (this can be a high-skill activity one handed in a hole in the wall.)
Pull cables up to have reasonable slack and cinch the cable tie to hold them in place.