The auction system allows you to finish bidding at auction and buy a player despite having insufficient cash in your account. You will have seven days to reach a positive balance again.
If you are unable to do so, bankruptcy proceedings will begin. Every day one of your best players will be sold to fill the gap, until the balance is redressed. You can stop losing your star players by decreasing win bonuses, selling players, signing sponsorship deals regularly or purchasing a cash injection.