Out-of-universe, Dementors were an avatar for Depression:
Winfrey: So you became depressed after your mother died?
Rowling: Yes, but I think it was a kind of delayed – I think I had
tendencies toward depression from quite young. It became really acute
when I was sort of twenty-five to twenty-eight was a dark time. It’s
that absence of feeling – and it’s even the absence of hope that you
can feel better. And it’s so difficult to describe to someone who’s
never been there because it’s not sadness. Sadness is – I know sadness
– sadness is not a bad thing. You know? To cry and to feel. But it’s
that cold absence of feeling – that really hollowed-out feeling.
That’s what the Dementors are. And it was because of my daughter that
I went and got help.
(Interview here; quote is from the end of section 4)
Their form is very similar to any number of generic things - ghosts, wraiths, that thing from Scream - but if you want to tie them to a classical cause, you have to step outside classical creatures and take them as an allegory for Depression.