You might be able to get a job in the same career, but you might have to start back at the bottom. I remember the chance cards winding up with a Sim getting fired quite a bit in Sims 3. In Sims 4, if you continuously do poorly on the job (go in a bad mood due to low needs, not do the extra home tasks, etc.) your performance could drop low enough where you get demoted or even fired. There's a reward trait that you can buy with Aspiration Points, Professional Slacker, that supposedly prevents demotion or firing, but I've never really tested it to see if it works.