I loved that series, until the last book. Maybe the novelty had worn off.
It's been a long time since I read it, but didn't the current Death decide to retire and pass the role on?
If you're referring to https://en.wikipedia.org/wiki/Under_a_Velvet_Cloak - note that it was written a couple decades after the prior books of the series, for a different publisher, to a different length. Those would be yellow flags with almost any author.
In "On A Pale Horse," Zane kills the current Death and assumes the role. I don't recall that he then steps down in a later book.