Image on left is from 4 days ago, but the pimple was slowly forming over around 2 weeks.
The goop was sticky, not oily. Earphones are Panasonic RP-TCM130.
I was not able to find an explanation.
Something to increase cable lifespan, lubrication, rubber disintegrating, sweat and earwax that somehow got into the cable, dielectric grease, SCP-1407, no clear answer.
At first I thought the wires just somehow twisted. Nope.
Have you verified the specs on OPs headphones?
Maybe I missed it but I don’t see where OP said this happened while connected to a phone.
They’re earbuds. You’re going to using them with a phone, maybe a laptop, or even in a pinch maybe a desktop. None of those output enough power to melt through a rubber cable without severely destroying themselves and never working again. OP would be posting “my phone exploded and I’m deaf now” not about the cable having a pimple.
Even my dedicated amp, a Shiit Magni outputs 6 watts with both channels combined, and ain’t nobody connecting shitty earbuds to an amp. The rest of the cable is going to sink away the heat from 6 watts before the rubber could get hot enough to melt.