The only way you can subdue a suspect is if he is fleeing from you. If he is firing back at you, you have no option but to shoot him down. For fleeing victims, if they are in a car, you will eventually cause them to wreck and take them in alive out of the wreckage. If the suspect is on foot, you can fire a warning shot (How to Fire a Warning Shot in LA Noire) or chase after them and tackle them (LA Noire Asphalt Jungle Achievement). Alternatively, if they are fleeing, if you keep chasing them far enough they will eventually stop.
