Jamieson-Fausset-Brown on Numbers 35:16
If he smite him with an instrument of iron, so that he die, &c.--Various cases are here enumerated in which the Goel or avenger was at liberty to take the life of the murderer; and every one of them proves a premeditated purpose.
Adam Clarke on Numbers 35:19
The revenger of blood - גאל הדם goel haddam, the redeemer of blood; the next in blood to him who was slain. See on Num 35:12 (note).
John Gill on Numbers 35:19
The revenger of blood himself shall slay the murderer,.... Not only shall have power to do it, but, as it seems, should be obliged to do it; be the executioner of the murderer; but not before his case has been heard, examined, tried, and judged; wherefore the Targum of Jonathan adds,"in judgment,''that is, as Onkelos explains it,"when he is condemned by judgment,''the court of judicature:
when he meeteth him he shall slay him; the first opportunity he has, even though, as Jarchi says, if he meets him in the midst of one of the cities of refuge, and no judgment is passed on him.
John Calvin on Numbers 35:9–end
Numbers 35:9-34
9. And the Lord spoke unto Moses, saying,
9. Et locutus est Jehova ad Mosen dicendo:
10. Speak unto the children of Israel, and say unto them, When ye be come over Jordan into the land of Canaan,
10. Alloquere filios Israel, et dicas eis, Quum transieritis Jordanem in terra Chanaan,
11. Then ye shall appoint you cities to be cities of refuge for you; that the slayer may flee thither, which killeth any person at unawares.
11. Constituetis vobis urbes: urbes autem refugii erunt vobis, quo fugiet homicida qui percusserit aliquem per errorem.
12. And they shall be unto you cities for refuge from the avenger; that the manslayer die not, until he stand before the congregati…
Read the whole note in the consoleKeil & Delitzsch on Numbers 35:19
The avenger of blood could put him to death, when he hit upon him, i.e., whenever and wherever he met with him.