Per the laws of the game a substitute may not enter the field until the player being replaced has left and the referee has beckoned the sub onto the field. What if anything should the referee do if the player currently on the field refuses to leave? i.e. sub reports to halfway, notifies AR that he wants to replace player #10 at the next opportunity. At next stoppage referee holds up the game to allow the substitution to take place but when called off the field #10 refuses to go off.USSF answer (March 13, 2007):
The referee has no authority to make the player leave if he or she does not wish to be substituted–see the IFAB/FIFA Q&A. That is a problem for the team officials. The referee must simply enforce the Laws of the Game correctly, but could exercise the proactive approach by asking the captain to assist in removing the player who has been substituted out.
This situation becomes a problem for the referee only if he or she has already allowed the substitute/new player to enter before the former player has left the field. That would make the substitution valid and present the referee with a headache in trying to clear up the mess. By allowing the substitute to enter the field before the player has left, the referee opens a can of worms that can never be returned to the can. Now the (former) player, if he or she refuses to leave, is guilty of misconduct. This means lots of paperwork for the referee, always a bad thing. Much better to enforce the Laws, in this case the requirements of Law 3 for a valid substitution.