I wish I would've kept track of the record, but a team I took over in Hall of Fame one season (Season 5) was out of it (I am positive it was below .500) & abandoned. I took that team mid-season, made some moves, got into 1st in the division and won the WS.
When I took over the team in the infamous Clarkson (another abandonment, totally decimated), it was in dead last in a division with a juggernaut, and I missed the WC by tiebreaker in that same season. That was no small task, considering what I had to work with.