They have a contract so if they don't want to leave then they can just sit here and twiddle their thumbs all they want.
Depending on the manager will depend on how the player is treated. Some will be told to go and train with the youth team, some will be told to only come in once the 1st team players have left and to train on their own, some will even be told they aren't allowed to use the same changing room as the first team players.
It then comes down to how stubborn a player is to whether they put up with it or bite the bullet and leave.
There is a saying amongst some players though which is 'No doe, no go' so they will tell a manager or a chairman he is happy to leave but the club have to pay his contract up.
Usually you will get a club and player meet half way and the player will get 6 months off his remaining year and then will leave.