They would have to do what any union does - leverage worker power. If the majority of Bandcamp engineers agreed to halt work until x demands are met, it would drive Bandcamp as a service into the ground. Tech workers also hold the keys to everything - they could take the site down, lock up the music, etc.

They maybe can’t prevent it, but they could leverage BC/Epic/whomever into providing some kind of decent severance for those left out in the cold. In theory.