You can bid with a debt. For example, you bid in the opening round on 2 players who are both worth 5M when you have a positive balance of 7M. You win the first auction for 8M. You are now in debt but since you already bid on the second player, you can continue to bid on him even though you lack the funds.

You can not place a new bid in the opening round of any auction (including free agents) when you have a negative balance.