Carlsen and Ivanchuk win Melody Amber.

I wonder, when was the last time a player lost six games but still managed to at least share the lead for the tournament?

Magnus Carlsen won thirteen games, lost six, and drew only three (!) in the 2010 Melody Amber tournament. He tied with Vassily Ivancuk for 1st with 14.5/22. In Bilbao points (three points for win, one point for draw), he scored 42 to Ivanchuk's 36.

Looking at the extended standings makes the feat less impressive. Against the bottom six in the standings, Carlsen scored 11.5/12, but against the top five, he only scored 3.0/10. By contrast, Ivanchuk did not lose a single game and finished 7.0/10 against the top 5.

Vladimir Kramnik finished in 3rd place with 13.0/22. Usually regarded as a careful and pragmatic player, like Carlsen, Kramnik finished with just a few draws, only five.