Conan is the boy Yelenika need and relieved with, what had happened can't be changed, waiting you is not revenge as it's hollow, but how you cope with it. Conan failed to save a criminal before so he knew what it feels to lose something, so he aims to not kill anyone else even if they had done serious bad things before, he calmed her and reawake her initial goal of everything. The moment Yelenika recognized Conan mirrored his lost son, she wouldn't able to pull the trigger on him, as it would mean she is losing her son yet again