How do the police use the citizens to try and catch Montag in Fahrenheit 451?
Society has been mobilized against Montag.
When Montag is on the run, the police put out a citizens alert to mobilize the public against him. They are hoping that they can make the public fear him as a dangerous criminal so that people will turn him in. He hears an announcement in the Seashell , the city is “talking to itself.”
"Police Alert. Wanted: Fugitive in city. Has committed murder and crimes against the State. Name: Guy Montag. Occupation: Fireman. Last seen . . ." (Part III)
Since citizens have been warned to watch for a man running alone, he knows that his behavior is suspicious. He has nowhere to hide. Anyone who actually knows him will turn him in at this point. His own wife turned him in. Beatty, his boss and friend wanted him dead, and now at this point even strangers will turn him in. He is not safe anywhere.
Nowhere. There was nowhere to go, no friend to turn to, really. Except Faber. And then he realized that he was indeed, running toward Faber's house, instinctively. But Faber couldn't hide him; it would be suicide even to try. (Part III)
His only hope is to find Faber, and try to find the book people and a better society, and a chance at a better life. Faber is the one civilized person that Montag has found. He met him as an old man sitting on a park bench. Montag knew he was different, and Faber trusted Montag enough to realize that he really did want to learn about books and change. Now Montag is on the run, trying to find Faber.
The only way to get away is to die. In the end, the man who dies is not Montag, but the police have to have a body for the public. They need a victory. So they tell everyone they got them. Montag dies, reborn anew, like a phoenix. Rising from the flames of society as it destroys itself, and rising from the flames of his old life.