They did have small overnight prisons where they kept the guy while they decide his fate.
mbachur, I don’t think that someone remains a Rodef forever after. I wonder if he is called a Rodef during planning stages; probably it only applies to actual heading to murder.
An answer to the Wolf’s question would be that there is no Halachic action on this person, but there are societal actions to be done. Just as setting up traffic rules and patterns are the responsibility of any government, it is not a Halacha per se (besides for Vinishmartem, Lo Saamod, Vechay Achicha Imach…).