There doesn’t seem to be many of them, probably because of the lack of commercial appeal, so there might extra pressure to make it great in an artistic way.
Sult/Svält (1966, Henning Carlsen) based on the novel by Knut Hamsun is the first one that comes to mind. Although it’s not in my Top 10 or 20 list, I seem to recommend this to people, because it’s fascinating, centered around this man who is intriguing, artistic (writer), but who is destitute. I don’t wanna put any spoilers out there, but here’s the IMDB link
I haven’t seen it yet, but I think Nomadland likely qualifies. From the reviews I’ve seen the protagonist prefers to call herself “houseless” rather than “homeless”, but I am pretty sure she’d be counted as homeless under most definitions.
Then there’s The Lady in the Van. Although I’m not sure if the real protagonist in that movie is Miss Shepherd (the lady who lives in the van) or Alan (the man who allows her to park her van in his driveway).
If I remember correctly, wasn’t Jean Valjean homeless for a short time at the beginning of Les Misérables? But he wasn’t homeless for most of the novel/play/film, so I don’t know if that qualifies or not.
The title character of Inside Llewyn Davis is functionally homeless - he has no home and no money, and basically couch-surfs with “friends” until they grow tired of him and kick him out. It’s not quite sleeping under a bridge, but that’s obviously his next step.
Not clearly great drama (tho the books are great fun!) but Jack Reacher is pretty famously homeless. Or IIRC for at least the earlier books.
And Hiassen’s Skink is homeless.
But in terms of “great drama”, the first and only character that came to mind was Magwitch in Great Expectations, and he’s not really the protagonist nor homeless throughout.
And I’ve lately been reading Shakespeare. He’s got plenty of characters living in forests, caves, etc. Not sure if that counts. But even Lear gave up his kingdom and planned on spending his time between his 2 daughters’ homes, until they kicked him out and he ended up on the heath. Not sure drama gets much greater than Lear!
Nightmare Alley (1947) – His long con a failure, Tyrone Power eludes the law by becoming a homeless alcoholic bum before finding employment with a circus (“Anyway, it’s only temporary, just until we can get a real geek.”)
The Fugitive Kind (1960) – Certainly not a great drama, but Marlon Brando makes an iconic wandering stud.
Yojimbo (1961) and pretty much every other samurai movie ever made featuring ronin (e.g., Lone Wolf and Cub).
The Tale of Zatoichi (1962) and all others in the series.
Fistful of Dollars (1964) and many a Spaghetti Western to follow.
Emperor of the North (1973) – Train hoboes vs. train conductor Ernest Borgnine.
They Live (1988) – Vagrant Roddy Piper uncovers alien plot.
