Do Jeopardy Losers Keep Money?
The Jeopardy "losers", i.e. 2nd and 3rd Place contestants do get to keep $2000 and $1000 respectively - even if they didn't "win" that much on the show. Though, given that they have to pay for their own airfare, travel and hotel accommodations it's more of a reimbursement a lot of times versus prize money.
In the rare event there is a tie after the Final Jeopardy round, the player with the higher dollar amount going into FJ will be awarded 2nd place.
In the even rarer event that those two contestants were tied going into FJ and tie after, the player with the higher amount going into Double Jeopardy would win 2nd place.
If there were still ties, this pattern continues until there was a milestone where one player was ahead of the other.