You would need to post what exact version of WatchOS is on your old Watch currently and what exact version of iOS they have on their iPhone specifically as well.
It would also be helpful if you posted what exact version of iOS you have on your own iPhone to see if you could help them that way and (thinking ahead) if you have any older iPhones with prior iOS versions available to you that you could (possibly) help them with that way.
In general, the Watch needs to been running the absolute final 'update' version of the previous compatible generation (with whatever iPhone) before it can be successfully 'upgraded' to the next generation. Here's a specific example: if you have iOS 13.x iPhone yourself and your old Watch was running WatchOS 6.1.x when you sold it and they have an iOS 14 device they can't update it, nor upgrade it, until the Watch is fully updated to the final 6.2.8 (via an iOS 13 device). Only then could their iOS 14 device upgrade from Watch 6.2.8 specifically (only) to WatchOS 7.x.
If your talking something even older... like WatchOS 5.x it'll probably need to be send to Apple for a factory update. Even in the scenario I describe above, it still may need to be sent back to Apple regardless. If you can post exact specifics though that would help figure out the next step, but the ultimate step is to get it sent back to Apple, even out-of-warranty, for a free factory update.
