Wire rope? Now I hope not because wire to rope splices are really old hat and one of the first things I got rid of on my
boat. They have a nasty habit of a loose wire coming out and catching hands like a
fish hook.
So when the line is pulled out to furl the sail, can you see a rope wire join or is it just rope all the way to the end attached to the drum? It should be.
Whilst the line is out measure it in diameter and length. If you have enough snip 12" off the loose end and take it to the chandlers to match once you have the length needed. Doesn't matter exactly the type or make, its a piece of rope so choose something comfortable to pull on and hold with bare hands and not too thick, hence taking a piece of the old rope with you.
Before you take the drum apart,
Google some of the other Schaefer models and You Tube to see how it comes apart. Next put a sheet or umbrella under the drum so when you drop something it doesn't go splash and ruin your day.
Look which way the old rope was coiled around the drum,
photo it if necessary and replace. Probably has a
knot, replace with a similar
knot.
Once replaced then think about greasing the drum and
head swivel too if they haven't been done this year. But read the manufacturers guides for the nearest one you can find first on how too.
Pete