They could just make you dead when your HP hit zero. How would that be?
Contrary to the ruleset of the game Larian said they were making?
Ideally, whether the AI does this or not should depend on the intelligence and/or behavior of the attacker. Animals tend to keep after prey until they're dead. Intelligent opponents might think it best to finish off any downed foe lest they get back into the fight (like you, me and probably everyone else would do). Or maybe they would see it best to go after the next immediate threat. Varied AI on the matter would be best.
Once someone is down, the ones remaining are bigger threats than the downed one. Sure, maybe some variance on this would work, but generally that should be rare. Such as if a character repeatedly is brought back from Downed, or the one who is constantly bringing people back up. Then maybe target that person for death to ensure that those downed stay down. But targeting someone helpless repeatedly when there are other characters actively attacking doesn't seem to make sense. Flee or Fight are higher priorities to Finishing.
Rarely going after downed players would help make it feel more like a tabletop experience, assuming the DM is not intending to unfairly dick over the players.