They are currently in a holding pattern right now.
Should note that they filed for the "good" kind of bankruptcy. Chapter 11 bankruptcy basically lets you sell shit off but allows you to ultimately walk away fully intact and more to the point, gives the owner full control over how they sell shit off.
Meaning, Denton could sell Kotaku and Jezebel and Deadspin off, plus dip into his own savings, to pay the amount of cash owed Hogan and keep Gawker going. Also, he can keep the business running and doesn't have to fire anyone.
Chapter 7 is the BAD kind of bankruptcy. The kind that means you are fucked beyond all repair and hope of being saved and you owe so much money, you don't even fucking have a right to save what you can or even be picky in how things are sold off to pay the debts.
If they had filed Chapter 7 bankruptcy, the court would force them to shut down EVERYTHING at Gawker and it's sub sites, because there is no fucking point in keeping them up and running since they are bleeding money they can't pay.
A trustee is appointed by the court and they basically are given the task to sell EVERYTHING that can be sold; the website, the offices, even office equipment, to get cash ASAP to pay off the debts (in this case, the Hogan verdict money). Denton could not say a damn thing and the Gawker office would be stripped of everything, copper wire included, for whatever the trustee could get for it, with the trustee not giving a shit who he sells it too so long as he gets paid.
Chapter 11 is basically "rehabilitation" bankruptcy since you can walk away from it relatively intact. Chapter 7 means you are irrevocably fucked and you can not be saved and are dead dead dead dead.
Should be noted that sometimes companies in Gawkers position will file for Chapter 11 but are forced to go into Chapter 7 by the courts. Granted, those scenarios don't fit the Gawker position, since that happens when a company owes MULTIPLE creditors and are basically already dying and can't be saved. Denton having the cash to pay the verdict money probably helps him out in this regard, as far as the fact that the court will most likely assume that after selling off several of the websites, Denton will "save" Gawker by breaking into his own bank account once he has Kotaku/Jezabel/Deadspin/etc sold, to cover the difference and keep the main Gawker website afloat.