Ok, this is actually an interesting question that i will overthink right now.
This is based not on my preferences, or what i think the character should do, but based on what we know from the characters.
First, let's assume, that they were in a fight with rules, like a sports, and that by attacking a KO'd opponent, the winner would still then be breaking the rules.
Now, i'm actually not going to give an answer only my favorite, but on all characters i can think:
Kasumi: She would teleport away and possibly try to recover a bit and would start fighting again, since begging or backing down aren't any traits shown by her.
Christie: she is an assassin, she would just pull out a gun and kill the person trying to attack her, she has no honor or dignity whatsoever.
Ayane: Similar space as christie, she is a ninja, and from the shady part of her village, once the rules of a fistfight were broken, she would use her ninja stuff, and no guarantees that the enemy would come out alive, since she has kunais and ninpo with her.
Leifang: too prideful to beg for mercy at this point in her life, would block all hits until she got completely defeated or found a way to fight back and win.
Momiji: Also ninja, also willing to kill, also with magic.
Phase 4: kasumi's personality but with hard coded in orders to kill every enemy, she will just use the blade and kill the enemy.