If it has began failing with no user intervention.. such as liquid damage/being dropped/sat on etc..etc.. Then yes it will be covered under warranty.
You could see whether your relative can remember where they bought the phone, or if not maybe ask a phone shop (or find out yourself) a direct number for Sony warranties/repairs.
As I'm fairly sure if the fault is as you described and has not been caused by user damage, then you can get it sorted, as long as the 1 year warranty has not been invalidated in any way.
