Bankruptcy in the US doesn't necessarily mean the end of the line.
If Gibson file for Chapter 11 they'll be protected from their creditors while they restructure the business, which could include selling off some of their subsidiaries and intellectual property rights from companies which they've acquired and ultimately wound up.
It also allows them to seek new finance.
Even if restructuring fails and no new finance is available then the creditors have the option of acquiring the company and it's assets in lieu of the debt. The chances are in that scenario the debtors would attempt to sell the Gibson brand and production facilities to a third party who could then acquire them without taking on the current debt.
Even if Gibson has to file for Chapter 7 bankruptcy, which basically means the complete liquidation of all assets, the brand and production facilities would still likely be sold as part of that process.
Gibson may be doomed in it's current form but I'd put money on the brand and the classic designs being in production, one way or another, for a very long time to come.