I suppose we might have seen it in some form after a couple years in limbo. It seems from the things Gygax and others have written that you probably had to have had some pretty deep pockets to buy TSR, even foundering as it was. Wizards had those deep pockets but I doubt anyone else could have come close.
I suppose the company would have gone under, then parts would be sold off to pay creditors. Whoever ended up with the D&D rights might have sold them, or sat on them. TSR did that with SPI, if I remember correctly. Maybe some other game company or group of people would have bought those rights but it would then depend on how much the creditor wanted for them. If they were willing to wash their hands of the affair, they might have been sold cheap enough.
As to who would have purchased the rights, and what would have happened afterwards, who knows?