If the trial was concluded when there was no high priest [in office], or if one kills a high priest, or a high priest that kills, [in these cases the manslayer] can never come away from that place [of refuge]. He [the manslayer] may not go out to bear witness, neither for cases having to do with a religious observance, nor to bear witness in a monetary suit, nor to bear witness in a capital case. Even should [all] Israel need him, and even a general like Yoav the son of Zeruiah, he may never go out, as it is said, “to there he fled”: ‘there’ must be his abode, ‘there’ his death, ‘there’ his burial. Just as the city affords asylum so does its Sabbath boundary afford asylum. If a manslayer went beyond the boundary [of the city] and the blood avenger found him: Rabbi Yose the Galilean says: “For the avenger it is a matter of obligation [to kill him]; for everyone else, a matter of option.” Rabbi Akiba says: “It is a matter of option for the avenger, and anyone else [who kills him] is not liable for doing so.” If a tree was standing within the boundary and its boughs extended beyond [the boundary] or if it was standing outside of the boundary and its boughs extended within, it wholly follows [the position of] the boughs. If he slew [someone] in that city [of refuge] he is banished from one neighborhood to another neighborhood. And a Levite is banished from one city to another.
Mishnah Torah 5:10
When a blood redeemer slays a person who killed unintentionally outside the Sabbath limits of his city of refuge, he is not held liable, as Deuteronomy 19:6 states: "He is not judged as liable to be executed."
רוֹצֵחַ בִּשְׁגָגָה שֶׁהֲרָגוֹ גּוֹאֵל הַדָּם חוּץ לִתְחוּם עִיר מִקְלָטוֹ פָּטוּר שֶׁנֶּאֱמַר (דברים יט ו) "וְלוֹ אֵין מִשְׁפַּט מָוֶת":
The above applies whether he kills him on the road before he enters his city of refuge or if he kills him when returning together with the two who are guarding him. If he enters his city of refuge and intentionally departs beyond its Sabbath boundaries,he has granted license for his life to be taken. The blood redeemer is permitted to kill him. And if another person kills him, that other person is not liable, as Numbers 35:27 states: "There is no liability for his blood."
אֶחָד הַהוֹרְגוֹ בַּדֶּרֶךְ קֹדֶם שֶׁיִּכָּנֵס לְעִיר מִקְלָט אוֹ שֶׁהֲרָגוֹ בַּחֲזִירָתוֹ עִם הַשְּׁנַיִם שֶׁשּׁוֹמְרִין אוֹתוֹ. נִכְנַס לְעִיר מִקְלָטוֹ וְיָצָא חוּץ לִתְחוּמָהּ בְּזָדוֹן הֲרֵי זֶה הִתִּיר עַצְמוֹ לְמִיתָה וּרְשׁוּת לְגוֹאֵל הַדָּם לְהָרְגוֹ. וְאִם הֲרָגוֹ כָּל אָדָם אֵין חַיָּבִין עָלָיו שֶׁנֶּאֱמַר (במדבר לה כז) "אֵין לוֹ דָּם":