Ask them what they want you to do about.
Be polite, it usually works.
If they demand a full refund ask was it working when they bought it.
Say it was working when you sent it and obviously only just stopped now.
We're not talking about brand new but used and secondhand.

If you feel like you should, perhaps offer a partial refund.
But TBH I would empahasise the fact it's 2nd hand and was working when you sent.
They have to prove that it was your fault and not theirs!

It's hard cheese really, and I'd be p**sed off but that's the way it goes!