It’s clear from the gemara above this one that the goel hadam has a chance to kill the rotzeach (whether shogeg or mazid) while he is traveling to the ir miklat. Two Talmidei Chachamim will accompany and try to convince him not to by saying acc. to the Maaratz Chayis, Hashem brought this about b’shogeg because the victim must have killed someone b’mazid previously and this man was just the unfortunate shaliach of Hashem to punish your relative, as the gamara says above also Hashem mazminim l’pundoc echad…
BTW How do you know that after the beis din is m’chayiv him misa he is “given to the goel hadam” although those are the words of the posuk here what about the gem in Sanhedrin Vahavta l’reecha going on the one being led out to be executed?