Let's say someone with a family, a marriage and children get embraced. This person don't care shit about Vampire politics or powers. So they take a night time job, feed from bags of donated blood and at home he keeps everything as it were just with a few restrictions, he doesn't even tell his wife about his condition because it's easy to hide.
I think of two scenarios, since he kept the secret Camarilla would let him live but would kill his family.
Or, if the prince is in a good mood, he would allow this to keep going if the entire family is embraced.