ERrm, you didn't say Mancini should just tear up his contract? Ignoring that, and assuming you did mean that, you would still end up paying him the length of his contract to "tear it up", but leaving him a free agent. Essentially if you've paid for him till say 2014, thats all there is too it, you can pay him in one lump sum and leave him able to sign for other teams, but you'll still pay him. What if, in 3 months he finally gets over his injury, but because you've released him, another club gets a 10mil player for free.
As you've paid him or WILL pay him, theres entirely no reason not to keep him till the contract is up, the biggest downside, is paying him exactly the same, the best possible outcome is he gets fit, is brilliant, world class and you keep him or he's decent enough, not first team but could sell him for 1-20mil. So biggest upside, great player, or loads of money, or a tiny bit of money, biggest downside..... none at all.
As for players, LOADS of players go through pretty awful injuries and just keep going, infact I can't name many players who give up a contract and don't battle on, again, its the career they've chosen and its highly paid, even at lower levels. Hargreaves say 80k a week at Utd is hardly a insignificant upside to the downside of being injured. I mean, think about it, you've broken your leg and knackered your knee's, you still want to get back to fitness even if you never play football again, because generally in life fitness, and lack of pain and things are fairly useful, getting paid to get healthy again isn't exactly a terrible burden footballers are under.