Are you sure it was bitten off or stepped on? Did it just kind of dry up, turn dark and fall off? If so, it is likely ergot. Ergot in the sow feed can pass through the milk and cause the piglets to lose circulation in their outer extremeties (normally makes the tail fall off). In severe cases it can have an effect on their feet as well. We've had some trouble this year with ergot and tails. I don't know if it is related to corn-quality or not but I suspect as much. Here's some info.: http://en.wikipedia.org/wiki/Ergot
As for your question, pigs with tails docked too short often times have a higher tendency of rectal prolapse. Other than that, they are not as attractive in the showring, but it won't stop a great pig from being placed where he belongs.