If a public company trading below NBV purchased back all of its outstanding shares without incurring debt, who would own the company?

Case in point Intel, was trading a bit above half book value at its nadir last year. Usually, this means that the company will be bought up and incorporated into another or sold for parts, a fate which Intel seems to have dodged.

But what if they'd sold off some major fabs to a competitor and repaid shareholders/creditors in full, who would own the company. It would be neither publicly nor privately owned.

I'm sure there are a million legal and regulatory hurdles to doing this in reality, but more from a theory perspective, it seems the remaining assets would just exist unowned.