These things die prematurely on headphones and any other place they appear.
The audio cable on this cassette adaptor died in an obvious way right by the connector.
Replacement connectors exist, but they aren't very good. I prefer to add a chunk of wire that already has a right-angle connector on it as seen in the following steps.
Step 1: Amputate the Diseased Limb and the Donor Limb
Leave plenty of wire on the connector side of the donor cable and the appliance side of the sick cable.
Step 2: Zip Cable
Step 3: Strip the Ends
This requires a light touch regardless of how you do it.
Bite through the outer insulation but not the inner conductors.
Pull off the outer insulation.
Step 4: Uh Oh
Looks like we'll have to "ring out" the cables to figure out which conductors to connect.
"Ring Out" means a conductivity test to see what pin connects to where.
First we'll strip the amputated connector.
I skinned away the strain relief with a knife to expose these stubs of wire.
These wires are insulated with a very thin coating of lacquer.
I scrape it off the tips with a knife.
Step 5: Ring Out
Figure out what connector pin is attached to which colored wire.
In this case it turns out red, blue, and clear lacquered wires do the same things in both cables.
Step 6: Strip the Other Wires
There are silky white fibers among the wires to make the cable stronger.
They'll melt and mess up your solder joints if you leave them hanging around.
Peel them out and cut them off.
Scrape the lacquer off the tips of all wires.
Step 7: Twist the Matching Wires Together
It looks like they'll all short out, but the thin lacquer coating is a decent insulator.
They won't short except where you've scraped the lacquer off at the tips.
The donor cable has single conductors. That's a sign of low quality and they won't last very long, even though I scavenged them off a first-class seat on my way out of the airplane.
Multi-stranded cables are much less prone to fatigue and break. The finer the conductors the better.
It's very important that you didn't nick those single conductors when stripping the cable. If they are nicked they'll break. Don't fidget with them.
Step 8: Solder the Wires
If you have some rosin-core solder and no soldering iron, a match or lighter will work just about as well.
But if you've got solder you'll probably have a soldering iron too.
Step 9: Insulate With Tape
After a few years it will dry out stop sticking so well, but it won't leave gunk all over like electrical tape will.
If I had some transparent shrinktube I might use that, but I think I like tape better for this fix.
It'll last longer than any other part of this project, and it's easy to see what's going on underneath it.
I folded a piece of it over the ends of the separated wires.
Step 10: Roll It Up
Step 11: Wire Ties
String, sinew, rubberbands, or nothing at all will also work.
That was a lot of steps, but that's pretty much what you have to do to fix one of these things.
It's hard work keeping stuff out of landfills.
enjoy your music!