What do you mean by "crosswind limit"?
If you mean the "maximum demonstrated crosswind" that you'll find in the POH, then, quite possibly, nothing will happen - depending on aircraft type. Many aircraft can be quite safely landed in crosswinds well above the demonstrated limit. The reason for the limit is often simply that this was the strongest wind the test-pilot could find to fly it. On the other hand, in some aircraft the max demonstrated crosswind really is a limit. The only way to know for sure is to speak to other pilots of that type of aircraft, or try it yourself if you're feeling brave enough.
However, if you do try this, and you bend the aeroplane, don't expect much sympathy from the insurance company.
Assuming you're approaching wing-low, you will simply run out of rudder authority at some point during the approach. When this happens, you add power, go around, and find somewhere else to land. So trying it is unlikely to cause you any problems, as long as you have an appropriate diversion lined up. Bear in mind, though, that as you slow down, the controls become less and less effective, so you will need progressively more rudder... if you're right on the stop as you start to flare, then you will run out of rudder during the flare, and that's going to be bad!
If you're de-crabbing, I'm not really sure what would happen, but I suspect that the aircraft will start to drift sideways by an unacceptable amount before it straightens up, which could well end up in a bent undercarriage. I don't particularlyl want to test this theory out.
FFF
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