וּמָצָ֤א אֹתוֹ֙ גֹּאֵ֣ל הַדָּ֔ם מִח֕וּץ לִגְב֖וּל עִ֣יר מִקְלָט֑וֹ וְרָצַ֞ח גֹּאֵ֤ל הַדָּם֙ אֶת־הָ֣רֹצֵ֔חַ אֵ֥ין ל֖וֹ דָּֽם׃
피를 보수하는 자가 도피성 지경 밖에서 그 살인자를 만나 죽일지라도 위하여 피흘린 죄가 없나니
Makkot
A murderer who exits the boundary etc.: The rabbis taught [in a baraisa], (Numbers 35,27) "And the goel hadam will kill the murderer" [we can derive that] it is a mitzvah in the hands of the goel hadam. If there is no goel hadam, it's permissible for anyone else. These are the words of Rebbi Yossi Hagalili. Rebbi Akiva says, It's permissible for the Goel Hadam, and anyone else is liable [for killing the murderer].
Makkot
He says like the following Tanna, that we learned in a baraisa, Rebbi Eliezer says, (Numbers 35, 12) "Untill he stands before a court for judgement" what is the Torah teaching us? Since it says (Numbers 35,27) "And the Goel Hadam will find the murderer" I might think that it means [he can kill him immediately] [therefore] the Torah teaches us "until he stand before a court for judgement"