odds of it happening eventually, go up the longer you live.
Despite this DNA replication being highly controlled and very accurate, the sheer number of times it is performed in the lifespan of a person (estimated to be 10,000 trillion times!) means the introduction of a significant number of errors into the DNA of some of our cells from this fundamental process is inevitable. source
Other way round: they are immortal because they don’t have transcription and replication errors.
Another point of view would be error replication leading to mutation since they cannot die. So a million years in the future how much different would they be from their original species.