When you buy a player, he will automatically be given a three day contract. Within these three days you must renew his contract, if you want to keep him. If you do not renew his contract, the player will leave your club some timer after the contract is expired.
If your balance is below one -1.000.000 Credits, your board will not allow you to renew contracts on players that require a wage. In this situation your only way out is to sell players until you have more than -1.000.000 Credits to keep the remaining players.