Moe Tilden: That cupcake makes a mess and we got a case again.
Ray Donlan: You know the difference between men and boys? Boys bet everything on everything! Boys think every hand is a royal flush! You play cards with a man, he knows his limits.
Moe Tilden: Can't do anything now! Hands are tied now.
Gary "Figgsy" Figgis: Listen to me, I got a check in my pocket for $200,000. I got a chance to start my life again. I don't give a shit about this town, I don't give a shit about that town and I don't give a shit about your fucking justice. Bein' right is not a bulletproof vest, Freddy.
Sheriff Freddy Heflin: I can't hear you Ray.
Moe Tilden: I gave you a chance to be a cop and you blew it.
Sheriff Freddy Heflin: You people are all the same.
Sheriff Freddy Heflin: What about Babitch?
Moe Tilden: What about him? Fuck him.
Sheriff Freddy Heflin: What about Donlan?
Moe Tilden: Fuck him too.
Sheriff Freddy Heflin: What about Joey Randone?
Moe Tilden: He fell off a building. Don't you read the papers?
Frank LaGunda: You're gonna be hurtin', Freddy. You're not gonna know when, you're not gonna know where. You're gonna be hurtin'. You mark my words - I'm watchin' you.
Figgs: Look Freddy, I say it's okay to be jealous. You save this girl's life, right? From it, from risking yourself, from saving her sorry ass, you go deaf as a result.
Sheriff Freddy Heflin: In one ear.
Figgs: In one ear. Then you have to watch this girl you saved, this beauty queen, marries this cocksucker.
Sheriff Freddy Heflin: I look at this town, and I don't like what I see.
Liz Randone: Why is it that you never got married Freddy?
Freddy Heflin: All the best girls were taken.
Moe Tilden: The case is closed, finished, over! Go to lunch! Go! Hey, go to lunch. Go to lunch! The case is closed. Everybody, get the fuck outta here. Get outta here! The case is fucking closed.
Figgs: Shut the fuck up, would ya, please? Sh - fuck.
Answer: I would think this would just have been random luck. There is no way you can just pay some random criminal to find and single out Joey and his partner to attack. With all the cops on patrol anyone of them could have responded to that call, so that was just pure luck that Joey and his partner encountered the criminal that threw him to his death on the roof.