I was watching Hellraiser (1987) today, and identified something that sounds like a sample that NIN used.

In particular it's the moaning sound that plays sometimes in conjunction with the female Cenobite. You can hear portions of it in this video, for example, at the 0:00, 0:22, and 0:34 marks:



And as for when NIN used it, I think it was used in the Hate Tour intro. You can hear several times starting at the 2:09 mark here:



You can also hear it at a similar point in the Dallas Video Bar show. Anyone else want to corroborate that match?