When Doctor Manhatten faced off with Rorschach, he actually just transported him to another part of the country. Seeing that he would'nt be able to do anything if he returned, Walter stayed and took on a new identity: Guerrero.
Today is the ninth anniversary of the cancellation of the DC television show that should be set in an alternate universe that is part of the Multiverse within the DCCU (Arrowverse) "Human Target".