If this is a "tractor-style" rider, and the shaft you mention heads down from the engine, it's what is called a "stack-pulley" which normally drives the mower and also the cutting deck, if that's so, then it sounds like the assembly has slid off the engine crankshaft, there should be a bolt going through the center of the bottom pulley up into the crankshaft which locks it into place, in any case, DON'T run the engine until you can verify if that's the case, the vibration could do some serious damage and even damage the crankshaft assembly and stack pulley further.