I believe that, in such cases, operator's first concern is to address the legal issue and not to hurry to shut down the business. If they are facing legal issues, their interest is to have them solved, as by functioning they would earn (obviously) more money than by not functioning, right? Having that in mind, I don't think that they will stop the signature campaign from the forum. Most likely, they will try to fix the legal issue then continue to function normally (this also includes running the signature campaign).
I believe that the campaign would be suspended only if they will be finally forced to completely shut down the business.