It's called senescence, when stressed cells can no longer divide to make new cells, and it's considered a factor in aging and in some diseases. Now scientists have some of the first evidence that at a younger age at least, senescent cells show up quickly after a major injury and are protective.
https://www.eurekalert.org/pub_releases/2020-09/mcog-scm092820.php
https://www.eurekalert.org/pub_releases/2020-09/mcog-scm092820.php