I was besieging a settlement owned by AI in single player (Immortal Empires).

The AI sallied out to defend during their turn and then lost the battle. Their attacking AI hero and its army survived partially, but the accompanying garrison was wiped out entirely. Since the AI lost, my siege continued through to my next turn.

Despite the AI being under siege and the AI's garrison being wiped out entirely, the garrison had refreshed fully and to full health. Additionally, the AI's hero lead army wasn't suffering attrition anymore even though the settlement was under siege (but it wasn't being refreshed either).