Units which lose a close combat must make a Morale check to hold their ground. If they fail, they must abandon the fight and fall back (see section 7). If they pass, the unit holds its ground and fights on. Basically, the combat is drawn, and no further account is made of the unit's defeat (apart from some good-natured taunting by the winner!).
Morale checks are covered in more detail in the Morale section of the rules (But the relevant ones have been placed here for ease of use).