Yes, but I've only seen it once - Roland Cheeseman resigned in 2022/23 season after getting my beloved Liverpool relegated for the 2nd year running - putting them in League One! I was surprised he wasn't sacked in all fairness!
I saw it in 05, then the guy in question then became his own successor a month later. I think I might have seen it in 08 but I don't pay too much attention to things like that so I can't think of any definite examples.