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.
You would be incorrect. If the power source shorts, it would heat the wires sufficiently.
And how much power do you think the DAC in a phone is going to output?
The built in DAC in a phone can barely drive my headphones, let alone melt a silicone cable. They typically output less than a watt. On a good day. Rubbers melting point is 365c and 1 watt isn't gonna do that.
Sounds optimistic. Checking a few USB to 3.5mm dongles, they seem to be around 25mW max at 32Ohms. Not sure how much that would change with short circuit, but I guess not much more.
It's more to do with wire gauge...
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.