You are right Tactician, clubs in real life do go in debt and they take loans and spend way more than they earn, but this is a game with no concept of loans or a bank from which you can take loans. You simply go into negative balance, who is club in debt to? How are clubs paying their players if there is no money? How do other clubs get their money from selling their own players if a person buying them is having a negative balance?
Anyone can do the same thing but to me it just feels like an exploit and something being used the way it was not supposed to be used.
I agree that first suggestion is a bit complex, but I dont see why it would complicate things too much to forbid to bid if you have a negative balance.
Maybe reduce time in which you can be in debt before the game starts selling your players? A week just feels too long.
Perhaps I am trying to make too much sense from a game.