The issue you guys have is your wage limit.
It's all good making Tiote and Cabaye the highest earners at your club but £7.50 a week isn't going to cut the mustard when Chelsea start whispering sweet £80k's in his agents ear. Regardless of what people think about loyalty, if you're earning £40k and another team offers you £100k you're going to leave, some will leave with a heavy heart but the first pay cheque normally takes care of that.
If you guys want to keep your top players you need to come up with a wage structure that will facilitate that, otherwise your dressing room will just be one very expensive carousel, albeit one that makes a lot of money.
I think we all know the reason your hairy CB won't sign a contract extension and that's because he's being asked to chop his wages in half, and for all of the decent performances he's put in...why should he satisfy the fat tumour that's in charge of your club rather than his own family?
In short....yes a player can refuse a move away. In reality this only happens to players who you actually want to leave your club, but they're staying on a good wage, sitting in your reserves knowing they'll probably never play for you again.