Me and my brother were talking about this and were wondering the last time this ever happened. That the two teams in the conference championship failed to make even the playoffs the next year. Last year the Wild and the Ducks were in the western confernce championship but neither is in the playoffs today. I'm sure it has happened but when?
I looked on hockeydb.com. It never happened (since expansion). In fact the only time the Western Conference Champion missed the playoff the next season was the LA Kings in '93. And then the closest we come is in 1996, when the Devils missed the playoffs after winning the Cup (which had been the first time that happened since 1970) and then the Caps missed the playoffs in 1999 after going to the finals (much like Carolina in 2003).
In the '80s 16 teams made the playoffs in a 21 team league so it was hard to do (although there were the strong Islander and Oiler teams). IN fact between 1983 and 1992, the Oilers failed to make the conference finals but twice. In fact (i just realized this), since entering the league the Oilers only missed the playoffs 6 times.