Much easier to prematurely end the campaign because the DM is "busy with a lot of stuff" but then he does a one shot with the exact same group minus one person - Then what do you know - The one shot went so well that they want to turn it into a full campaign. Oh but, they invited a new player who is joining their new campaign and its the "just right" amount of players and they can't really add anyone else right now, especially the person excluded, but maybe next time?
Edit: This is intended to be mostly sarcastic as this is a real funky thing to do. Ideally if you have a problem player, its better to talk it out and either solve the problem or end it on understood terms.