Do people still say "dassent" in the rural Southern US?

It’s an old-fashioned word that means “dared not.” I don’t think it’s specific to the South.

I've never heard of it

I grew up in the south (Alabama) in a pretty rural area and I’ve never heard that word in my life, so I’m going to say no it is not still used today.

No. As someone from Mississippi, I would hear "Pa don't dare sweat" or "Pa doesn't dare sweat," with "doesn't" pronounced like "dudn't." Most long S's in Mississippi are either not pronounced or are turned into D sounds. Mississippi, for instance, is usually pronounced Missuh-ipp-ee.

To answer your question, today that usage of “dare” would be perceived as old-fashioned and/or formal throughout the US. I also don’t understand the other commenters saying that “does not” makes more sense than “dares not” — the rest of the sentence is about the dire consequences Pa believes will ensue if he does sweat, so saying that he *dares not sweat* is clearly the better option.

People say “doesn’t” and it sounds like this but never seen it spelled out like this other than Faulkner. (Lived in US South for 15 years) You’ll see other examples of this in Mark Twain’s and some Steinbeck I believe.

I could tell it meant "dares not", but only because I've seen "dursn't" and this looks like an alternate (or maybe eye dialect) spelling of that. I'm not from Mississippi, but I am southern, and I've never heard the word before. I only know "dursn't" from literature.

I have never heard it in my life

californian here and i don't recall ever seeing or hearing that word

No

I’ve heard “darrent” which isn’t quite the same but has the same meaning I believe 

From your sample it seems to be an intentional misspelling of *doesn't*, to indicate that a character has an accent.

I grew up in the South and I've never even heard that word before. I'd bet it's meant to imitate the accent. "Doesn't" in a deep Mississippi accent would sound like "dassent"

I’ve never heard pronounced that way. Born and raised and lived my entire life in the South. I’m also not convinced that “dassent” ever been a real thing. Sometimes, authors used to write out the way people talked in an accent by spelling each word phonetically, especially characters speaking in a Southern accent. You often see it when they were writing down the speech of Black characters. Mark Twain did this and it’s awful to read, IMO. I haven’t read much Faulkner, but he may have been doing the same. It doesn’t mean people were literally using a different word back then - it was just the author deciding to spell the word in a weird phonetic way to emphasize that the character was speaking in a different accent.

I believe that’s just a way of spelling out the accented pronunciation of the word “doesn’t” rather than a word of its own.

I’ve lived in Arkansas, Tennessee, Alabama, and North Florida. Never heard this before in my life.