Typically no, because employees 'sell' their rights to the patent to their employer when filing the patent application. It is customary for the employees to get a silver dollar as a token that has monetary value (hence the sale) and we can thank Richard Feynman for forcing there to be an actual transfer of money :)

I should also add that usually the inventor can't take the patent to their next job but if the inventor wrote super-narrow claims into the patent then that would be easy to work around at a future employer.