Well, two of them were nobodies overnight, but I wouldn't say Bernie Nicholls "went south" quickly. He waited 30+ games before joining the Oilers, but when he arrived he helped them a great deal and scored a point-per-game. He had great chemistry with Vince Damphousse, who unfortunately wanted out after that one (1991-92) season. The Oilers went completely into the tank in 1992-93, but when healthy Nicholls still had the best per-game stats on the team with 40 points in 46 games. He then had a similar year in '94 with defence-first New Jersey, but he came back to life in Chicago. He comfortably led the Hawks in scoring in 1995 (and had 12 points in the playoffs as they went to the third round), then had 60 points in 59 games the next year, the best per-game on the team again (well, matching Roenick), and another 9 points in 10 playoff games.
So, he scored 110 points in 108 games for the Hawks in 1995-1996, the best per-game on the team, and another 21 points in the playoffs. In fact, in 1995, he finished 12th in NHL scoring, ahead of Gretzky, Hull, and Selanne.
So, he wasn't finished in 1991.
(I feel like I'm always defending Bernie Nicholls... well, someone has to!)