It did, it was just called a gambeson/jupon/aketon depending on the time and place. Both gambesons and linothoraxs were heavily quilted cloth, usually linen, worn as a standalone body defense (there is some debate as to what linothoraxs were made from, either leather or linen). It is believed that the armour was arrow and cut resistant and provided moderate defense against piercing attacks as well. The defense against blunt force attacks such as maces would be limited on it's own due to its inability to disperse the force over a large area, but under mail or plate it would be much better at absorbing the dispersed force.
Most early plate was worn over a light jupon, or sometimes under one. at least in the later times a gambeson was worn under maille, but there is no documentation for the early middle ages, though many still suspect that it was worn, but nothing was written about it.