The name of the passive is called
PASSIVE_PANTIES_STRIPPED_ONE_ID
. The more advanced versions are not in the game yet. You unlock the passive after having your panties stripped at least 5 times and reaching slut level 10. Your panties are stripped in all sex scenes (this includes non-penetration scenes like handjob or cunnilingus scenes). Also you only see that the panties are missing, if your clothes are (partially) damaged. With the passive, you have a 10% chance to lose the panties for the rest of the day after they got stripped in a fight.
Yes. In the beginning the best option is to use the skill that increases evasion chance, because this allows the enemies to damage you until you have no stamina. The 'give up' skill that was meant is unlocked by the passive 'Convenient sex object' that you get by having 30 sex partners and reaching max desire in all five categories at the same time in at least 4 battles. The 'give up' skill sets your stamina to 0 instantly.