That's true. They might even have a hard time even keeping it up for a couple of weeks if said institution doesn't even bother to respond to the twitter mob, just completely ignores them. Social media has a very short attention span, and if nothing new happens, they'll move on to something else to get outraged about.

It's still problematic that many people will lose their livelihood and have their careers damaged by this. Even if your current employer sides with you, having negative twitter mobs write about you might reduce your chances of landing the next job.

In order to make things better, I think we need to be more vocal and forceful in standing up to cancel culture. To actively reject it as a society. Just hoping that your current and future employers will maybe side with you, maybe that's a start, but it isn't enough.