What do you think happens to him after you've completed the level? Think maybe he gets killed or perhaps one of Starkweather's men gives him a bottle of beer and sends him on his way? I'd like to think the latter. Not like Tramp was a threat, and why waste a bullet on him?
shareKnowing Starkweather, the tramp would have been killed, because he was a witness to what was going on. Just because he was dead drunk doesn't mean he couldn't remember anything and put two and two together. Remember what happened to Cash's family after he rescued them. UNLESS... unless the tramp really is a lunatic called the Scarecrow, as it shows in the notes in the game. If so, Starkweather would likely have a use for him in one of his future "productions."
"Just repeat to yourself, 'It's just a show; I should really just relax.'"
It's strongly hinted that the Tramp is the lunatic/twisted alter ego of Scarecrow, a scraped role that was originally set to take part in the game. You can read his back story in the Special Features menu, with the storyboards, concept art, gallery, etc. And his biographical story strongly hints that he is the Tramp.
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And I miss you, like the deserts miss the rain.
I know I'm very late to the party but I just have to put my two cents in. The link between the tramp and Scarecrow is very fascinating; I've never put together that they were the same person.
I actually had my own hypothesis for the tramp. I believe him to be in Max Payne 3, in one of the Hoboken/New Jersey flashback missions. (Very minor spoilers ahead.) When Max is on the run from the mobsters in his apartment complex, an older hobo-esque guy, Max's neighbor, runs out at the mobsters, shouting insane things. (I do not recall the exact things said, though. It is a farcry from drunken mumblings, but a lifetime of booze and regret can cause such rage.) He sacrifices himself, killing the mobsters with explosives that were on his person. As Max, the player can go through the newly deceased hobo's apartment, and nothing in said apartment points to a healthy state of mind; it can very well be the tramp from Manhunt. Hoboken would arguably not be too far from Carcer City, which we can infer is in New York, as it was stated that it is within the same state that Liberty City is in.
Like I said, just my two cents.