If the initial filing _mistakenly_ left out an inventor, then their correction of inventorship is likely to be seen as fixing the problem. This could even be a situation where an assignee left someone's name off because they, without deceptive intent, truly thought that person was not an inventor and were later convinced they were in error. Such situations can be corrected during prosecution, or through a certificate of correction if the patent has already been granted.
If the initial filing _deliberately_ left out an inventor with deceptive intent, then in litigation it is likely that the patent will be held unenforceable. Unfortunately, that outcome, while justly deserved for the perpetrators of the fraud, does not result in the remedy most spurned inventors are looking for. "If I can't have it, neither can you" may be the best they can hope for. To my knowledge there is no mechanism for a spurned inventor to share in the benefit of a granted patent. 35 USC 256 allows for correction, but the circumstances, even if "without any deceptive intention on his [the spurned inventor's] part", still require that the inventor was left off the patent "through error".
The answer to your assignment question may depend on the jurisdiction in which the assignment was made, so I would consult an attorney competent in that jurisdiction.