If you did burn out a rheostat it would do one of two things:
1) Disconnect the fan
2) Stop resisting at all and push the fan to normal speed again.
2) isn't a problem, it just gets a bit louder. 1) is, so when you wire a rheostat some people hook up the third lead to the the same wire as the 2nd. Sorry I can't explain it better, I have to goto work, but basically that way if the varable part of the resistor fails current can still flow through the fixed amount (not much, but on smaller units enough to move the fan).
It can't short because it has only positive or negative, but not both.
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