They didn't buy the company, they bought some of the assets. In an asset purchase you don't take on the liability of the company your purchasing the assets from. Pebble as a company will go into bankruptcy and cease to exist.
There's probably some startupy term for this. If Fitbit and Pebble were both buildings next to each other, Fitbit just bought Pebble's to demolish it and build Fitbit Tower 2.
But I also read that the employee-shares would be worthless, so it looks like FitBit bought Pebble in a weird sense.