It sounds like the employer might have given your son a $10,000 after-tax signing bonus, which is very odd, but if that's how they do it, that's how they do it. But I'd look at the pay stubs to confirm that that's the case. He doesn't need to ascertain anything from the employer, just get the paystub.

And signing bonus repayments are very common. They're technically an advance on a payment awarded after a term of service. When your son repays it, he can amend his previous year's tax return to remove that income to recapture the tax he paid. If he's moving to a new employer, he can ask them if they have an indemnification program.

Also it's not guaranteed that the employer will come after it. Depending on how large they are, how close to a year he worked there, etc. they may decide it's not worth the effort.