In game 5, Kim was in his 2nd inning of relief when he allowed the Yankees to tie, and 3rd when they won the game in the 10th. Then he was brought out again the following night. Kim was ground into the dirt by Brenly all season (he nearly eclipsed 100 innings as a reliever), and they probably win that series in 5 if they had someone other than Greg Swindell and Mike Morgan as the setup men. 2002 he bounced back just fine, with (if I recall correctly) back-to-back series in which he clowned the Sox at Fenway, and finally got his save at Yankee Stadium (which culminated in him celebrating by tossing the game ball from the infield out of the playing field in RF).
I really can't fathom why someone wouldn't A: not wanted to trade for him, and B: not be happy with his ripple effect as it related to the bullpen. That move saved the season on two fronts, as it settled the bullpen, and got at bats away from the painfully mediocre Shea and gave them to Bill Mueller and David Ortiz.
edit - my memory was a tiny bit off, he threw the ball into Monument Park.