My Solution
My furler is a Profurl but most furlers suffer this problem because, although one keeps tension on the line whilst unfurling and cleats it off when the sail is fully open, when the boat turns downwind and the jib/genoa alternately flops from side to side it causes a half turn of slack to develop. If this process continues then inevitably a turn gets over the lower lip of the drum.
It can also happen whilst tacking too.
There is quite a bit of force involved as you will discover if you try to hold the luff spar whilst this is happening. This force is easily sufficient to force the reefing line between drum lip and the protective cage or tube.
I got caught like this after a 60 mile downwind ski ride. Single handed I was in real trouble trying to furl the sail whilst the boat leaped from wave to wave. With everything up I dared not turn into wind and the tricky Needles Channel at full ebb was to leeward.
The three photos show what I made to ensure this could never happen again. No. 1 is as original. No. 2 is the ring & No. 3 is with the ring in place.
The aluminium ring fits ON TOP of the lower flange of the reefing drum. It is retained by the four vertical rods of the cage and, as it is a loose sliding fit on these rods, it rubs on the top of the lower flange.
My photo is dated March 2002 so there has been no incidence of this difficulty since then.
As an alternative, and before I made the ring, I put a small block on the reefing line with a foot of bungee up to the lower lifeline. When unreefing I pulled the line taught as normal and the bungee kept some tension on the line whilst the boat tacked and gybed.
Drawings available for any Profurlers just PM me.