Having had a few pairs go like that and the hatred I have for the tinny weeny sub-hair micron strands of wire they have and fixing them. I always go for headphones with a socket connection or if hard-wired, have a second output jack that you can use to share with a friend who can plug in - as the way those are wired, you can just plug a male to male cable in and use that as the headphone input.
As for Bluetooth headphones, I go for ones which can also accept a hard-wired connection, so at least it prolongs their life if replacing the battery proves an effort beyond the scope of my elephant-hands.
I used sennheiser HD201s ($15 canadian on sale) for years until the cable broke, then upgraded to sennheiser HD599 ($149 canadian, on sale) because it has replaceable cable. Might add an aux jack to the old ones, sometime...
I ended up with bose QC25 which can be found used for $50-90 because it sounds good, is comfortable to wear, has a replaceable cable, replacable ear cups, and although it uses a battery for noise cancelation its a plane jane nimh rechargable aaa battery sold all over creation. Also the battery running down just means noise cancellation stops working not sound.
I find it amusing that the headphones people are upgrading to in the same product line are exclusively bluetooth meaning more hassle connecting, lower quality sound depending on phone and codec supported, aren't able to produce sound at all if the battery runs down and to add insult to injury the battery is built in and hard to replace. It's one more thing you need to constantly remember to keep charged up so it doesn't die when you need it with a hard to replace part that is going to go bad far sooner than the device gives out. Ifixit rates it hard and says it takes at least 45 minutes and a $30 part even if you have all the tools.
I spend far more on beans annually than I have on hardware in the past 5 years. I have zero interest in chasing more expensive hardware for a fix. But I did actually upgrade my headphones to Sennheiser hd599 when the aux cable in my old pair broke.