The healing gauge is the feature that was first implemented in Power Instinct Matrimelee and has been a staple since.
When the fighter is hit by attacks, a portion of this red meter will appear in the health bar. As long as the damaged fighter isn't attacked, health will gradually replenish over this bar until it's filled up. The more damaging the attack, the more of the healing bar will appear.
It's important to note that if the player doesn't safely roll to their feet when knocked down, this meter will disappear, encouraging players to learn to properly time their saving rolls to prevent this in order to last through the round longer. If the stress meter is filled while there is still a part of the healing meter remaining, the stress flame will restore it to full immediately.
Something of this sort was also featured in Rage of the Dragons, though it worked differently in that the damaged fighter would heal only when not in play.