The previous mafia boss was the one who had the “older man Kouyou admired” killed for running away. My guess would be that Kouyou was still young enough to be trained and her ability was valuable enough that the mafia boss let her live. He probably also thought that by killing the man he would both remove his influence on Kouyou and effectively traumatize Kouyou to the point she would never try and run away again… or else.
But that’s only my guess. Too bad Kouyou isn’t a bigger character so we could get more information on her past (I could say the same for ALL the mafia characters!)