Is being an animator/storyboard artist a stable job? Aren't

>Aren't they technically out of work whenever a show gets abruptly cancelled

Only if the cancellation of said show is putting the studio itself out of business. Otherwise, they'd just start working on the next show they have lined up. It would be a really expensive process for animation studios to completely re-hire an entirely new animation department each time they start a new project.

Yes but a lot of them are situated in LA already, where most of these jobs are

>Is being an animator/storyboard artist a stable job?

No.

> Aren't they technically out of work whenever a show gets abruptly cancelled(which happens a lot these days)

Yes. With a few exceptions, if you work in the animation industry you will end up jumping around between a lot of different studios over the course of a career.

You're hired for a project, not as a permanent resident of the studio, unless you're part of the core team that stays in that studio, or just very,very good. Even then you'll probably jump around as new opportunities come along.