Homer

"You just gotta think like a rat, see? A rat's vermin, but he knows how to survive. How to... stay out of the rain.
 * —Homer to Murphy regarding the subway access tunnels"

Homer is a minor character in Silent Hill: Downpour. He is an elderly homeless man lurking in Silent Hill's Pearl Creek subway station, seemingly trapped in the Fog World. Homer offers Murphy Pendleton several fetch quests, upon completion of which Murphy is allowed access to the subway tunnels: an efficient and relatively safe way of quickly traversing Silent Hill.

Biography
Homer appears to be a former prisoner, perhaps from the Ryall State Prison much like Murphy, because of the shackle rings attached to his clothes which bear a striking similarity to Murphy's prison jumpsuit. This is further strengthened by his comments regarding the tunnels. He tells Murphy that one has to be like vermin to survive, then he'd be fine "just like old Homer". One possible escaped prisoner to another, this statement likely gave Murphy a depressing glimpse of what the rest of his future could be reduced to: forgotten, scavenging vagabond, dying alone in the dank underbelly of an unassuming small town.

Silent Hill: Downpour
Once Homer is located in the subway, he will be able to help Murphy by unlocking subway access tunnels. This gives Murphy the ability to quickly traverse around Silent Hill. Homer will do this in exchange for several items including a candy bar, a coat, and a fishing rod. Together, these quests make up the "Homeless" sidequest.

If Murphy gives him all of the items he asks for and returns later, he seems to be lying dead or unconscious on the floor (likely the former given the presence of Dolls in the tunnels).

Symbolism
Homer is portrayed as having a past that has potentially damned him to life (and possible death) in Silent Hill. This is suggested by multiple characters in Downpour, such as Howard Blackwood, Bobby Ricks, and John P. Sater (as well as Murphy himself in the "Full Circle" ending). This essentially makes Silent Hill a kind of purgatory, where the guilty are punished for their "sins" until they can face and overcome them - a theme which has been prevalent in the series since Silent Hill 2. Failure to do so results in the individual being stuck in a never-ending "loop". In the case of Homer, he is either unwilling or unable to proactively help himself, instead relying on Murphy to provide him with the basics he needs to survive, such as warmth and food. After Murphy finishes retrieving his final requested item, the fishing rod, Homer simply lies down and either dies, or falls asleep - obviously not utilizing the rod for its intended purpose, despite Homer claiming that he wants to avoid living like some "scavenger". This parallels the vermin that Homer identifies with: rats who parasitically feed off of the hard work of others and contribute little to nothing positive to human society.

It is also possible that Homer is a representation of how some people view the homeless - the achievement/trophy that players receive for completing his quest "Will Work For Food" (a sign commonly toted by the homeless and unemployed), seems to point to this being the case. It is important to note however that Homer does not seem to "work" at all, even to feed and clothe himself.

His name may be a sly pun on the fact that he is homeless.

Homer's eyes in the Achievement image give the impression of being filmed over, as though he were blind. This could be a subtle reference to the Greek poet Homer, author of the Iliad and the Odyssey, but could be coincidental. Furthermore, in Greek symbolism, physical blindness was normally offset by unique wisdom as compensation; the blind had an internal type of "sight" beyond human understanding. The Homer of the game shows a wisdom for survival, and allows Murphy access to an alternative, "wiser" route throughout Silent Hill. Subway tunnels are also technically unseen, since they are underground.