The mayor is elected unless there's a vacancy in the office.
I've been away for some time but it happened twice when I lived in the area. First, when Pete Flaherty left to take a job in the Carter administration, and then when Flaherty's successor Richard Caliguiri passed (late 1980's, I think) from complications due to amyloidosis.
As I recall, Caliguiri had to pledge to not run for reelection as mayor in order to get the council presidency. Flaherty had been an early supporter of Carter, and it was widely expected he would get a job in the Carter administration (turned out to be deputy attorney general). But then when it came time to run for reelection, Caliguiri did not stick to his pledge. That must have been '77. Caliguiri was reelected in '81 and '85 -- not sure about '89.
He was succeeded by Sophie Masloff -- I remember her mispronouncing many of the Pittsburgh Penguins' names (that was part of her charm), and they won the cup in '90 and '91.
I'm from Pittsburgh,people here are die hard democrats,they have a strong hold on the city.I believe at one time the area in the city that I once lived in we were the only Republicans.
You are correct - he died in 1988, while in office. Mrs. Fury was a cousin of Richard Caliguiri, I understand he was well generally well-liked.