This trope seems to be invoked when showcasing rural slovenly yahoos; Wreck-It Ralph is the most recent example that comes to mind. Is it just to suggest a general lack of sartorial neatness or is there some legitimate reason why someone would wear them half-strapped?
It’s not an uncommon style. In the 90’s it was even a popular style. Do a google image search for 90’s overalls and you’ll get plenty of hits. Including this one:
I’ve worn mine with only one strap several times because the buckle on the other side is broken.
Sometimes called a ‘Jethro’.
Almost all hillbilly tropes date back to Li’l Abner.
He looks like he’s wearing a corset and pin-striped trousers there. Frankly peculiar.
My totally facetious theories, based upon observing the character Old Man Crenshaw from Boggy Creek II: And The Legend Continues (MST3K version):
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Using one strap takes less time, thus saving minutes over the lifetime of the garment.
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Using one strap takes less effort, therefore saving energy and reducing muscle stress.
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By using only one strap, you have a backup when the fabric or fastener breaks or wears out.
It’s laziness at worst.
My guys wear coveralls that are bibs with straps. Coat on top, during hunting season/cool weather.
I’ve only seen them doing it in the evening.
Especially when you need to pull down the overalls, e.g., to sit on the toilet. With just one strap fastened, you can often make the process even quicker by slipping the single strap on and off your shoulder rather than unhooking it.
Like untied shoelaces, half-fastened overall straps do about 90% of the job you need them to do, for 50% or less of the effort required to adjust them “properly”.
That hangin’ strap may end up wet or worse. Gotta be careful.
There’s woman who comes to my store; I think she wears bib shorts almost every day with one strap undone. I think it’s a style for her. Her hair is always done, she wears make-up which is always done. She is always neat and tidy. I dunno’ I guess she likes it.
I’d say this is it. They are supposed to look like they’re so poor they can’t afford clothes that aren’t worn out.
Not that I’m saying scabpicker is poor! They might just be frugal! 
You gotta cut a guy’s clothes some slack when his life has been flipped, turned upside down.
Haven’t tried it but I think it will work better than regular suspenders which always slip off my shoulders.
I’ve seen people fasten the loose strap to a waist button, so it’s not coming over the shoulder to support the bib, but also not just flapping around.
That’s a style preference. You ain’t seen 6-pack Jimmy-joe doing that down at the local Greasy Bar and grill.
(Do not order the cheesy fries and a draft beer.)
My GF in college wore it like that…damn sexy. 'Specialy when there was nothing underneath.
Wait. You gotta have something underneath.
Half the bib flips down.
And side-boob ain’t an issue no more. It’s full frontal.
I hope y’all were indoors.
These were, shall we say, private times. Although there was that one time of strip poker.
It’s a deliberate fashion choice. My 24-year-old daughter wears her overalls like this, and it’s super cute.