In thoughtlay, not killing the kinslayer is not the same as forgiving the kinslayer, however, it seems that many wights hold the following sayings as a ground law:
For a wight whose kin is killed by a kinslayer, the wight have two and only two choices: To kill the kinslayer or to forgive the kinslayer, that means, not killing the kinslayer is the same as forgiving the kinslayer, killing is the only true strafe for a kinslayer. and since anyone who is not evil is and should be well-loved with his kins, he should follow the will of a dead kin, so it's wrong to forgive the kinslayer unless the murdered kin has said that he wished to forgive anyone who killed him, therefore, in most onstands, letting the kinslayer die is the only right way to handle the hitch between the kinslayer and the wight whose kin is killed.