The purpose of a clutch is to allow some slip while engaging. This is why compressors are connected to the drive pulley through a clutch and not simple gears. By using a clutch the compressor comes up to speed slowly enough to avoid damage from sudden accelleration. Same thing for a manual shift transmission.
I'm not entirely sure what you are asking here, but I can tell you that the most common cause of a failed car compressor is lack of lubricant. This happens when there is a refrigerant leak in the system. See www.aa1car.com/library/2003/ic50350.htm for details and talk to a mechanic about it for advice.