One headphone sound went out

If the headset has a detachable cable, check that first.

Otherwise, it could be an issue with the driver or the board delivering the signal to the drivers. In this case, sourcing replacement parts would be challenging to say the least.

First thing to do of course is to plug in a working headset. If both channels OK this will eliminate the headphone output socket as the culprit. Then it's time to test the faulty headpgones' speakers and plug individually as explained below.

You only mention the cables going to the headphones themselves. Have you checked the headphone plug? This is normally a moulded 3.5mm banana plug with 3 separate metal contact bands.

If this is a molded plug it often has a broken wire from many ins and outs. If able to open a non-molded plug, you will be able to spot the open connection/broken lead and repair it.

With a molded plug you will not be able to spot the break from the outside but can easily test it using a multimeter (switched to the low ohm scale) or even a 1.5V penlight (AA or AAA) cell. The method is as follows

PS: polarity is unimportant.

Place one lead of the mm or cell-terminal on the plug contact band -the broader one at the plug end, which is the common or ground connector.

Now put on the EPs on and touch the other mm lead (cell terminal) to first the plug's centre contact band and then to the plug's end contact.

This tests for wire continuity from the plug to the speakers and if OK you should hear a 'scratcing' sound each time you momentarily touch the contact. The contact that doesn't produce a sound is the one with the broken wire. In your case only one speaker should sound. This indicates the plug is at fault. Just cut off the moulded plug and replace with one you are able to solder the leads to bearing in mind that the screen should go to the connecting band lug closest to the body of the plug namely the common/Earth lead.

The other two wires connect to the other two lugs. Which one goes to which lug is really not important as far as which channel is left and which is right.

As a last thought. To make sure it is the plug and not the speaker, If only one speaker responds using above method then test the non sounding speaker by connecting the terminals directly to it's lugs. If no scratching sound is heard (or the speaker cone doesn't move) the speaker is dudd and needs replacing - although this is rarely the case.