I have a relative who just received a tax refund check in the mail, it's well over two thousand dollars. The only thing is this person has not worked in about 3 years and has not paid taxes since then. Is this simply a mistake?

It could be for a year long past, it could be a mistake, it could be a scam and isn't a real check. It isn't easy to answer questions second hand.
The IRS doesn't send refunds if someone doesn't file. There are certain ways to get back more than was paid in taxes if someone does file, but that's about it.

There are deductions and there are credits. If your relative qualified for tax credits, then they may be entitled to money from the IRS (not a refund). But they would have to file to receive that money. The only way to get a refund is to over pay (usually from withholding) what they actually owe in taxes.

Your relative may have income that you are unaware if, on which he has made tax payments and is just receiving a refund.

If he is attending school, he can get up to $2,500 for the American Opportunity Credit.

He may be getting the Earned Income Credit.

That is only a few of the possibilities.