TT #216 · Parashas Shoftim · Fifth Aliyah · Passuk 19:10
So that innocent blood not be shed in the midst of your land that the Eternal your God is giving you as an inheritance, and blood be upon you.
Torah Temimah points to Sifrei Devarim 185 / Makkos.
TT lemma: וְלֹא יִשָּׁפֵךְ דָּם נָקִי.
Sefaria — Sifrei Devarim 185 / Makkos
English: ‘So that innocent blood not be shed’ – this is the blood of the accidental killer.
Derash on the purpose of the institution (Sifrei) — protecting the accidental killer prevents blood-guilt on the land.
The cities of refuge exist so that the blood of the accidental killer is not shed, and so that blood-guilt does not rest on the land.