No hard fork will be introduced unless it's clear who will win. It's extremely unlikely that we'd come to a point where anything close enough to an exact split would happen. As long as there's even a 60-40 majority, once the fork happens most people would abandon the smaller fork, though it might live on as a tiny alt-coin (even if that alt-coin is technically the original protocol).

The holdouts would call the losing fork the "true Bitcoin" and have some other name for the majority fork, and the rest of the world would carry on as if nothing, after a few hickups and probably a medium-term price crash while people learned to stop thinking in terms of "Bitcoin" but instead in terms of "the de facto standard currency protocol of the internet."