The rear end oil pump is driven off the pinion shaft with a small belt. I thought the engine oil pump was on the front of the engine but the power steering pump is there also. It could be something as small as a chunk of tire rubber that dislodged the belt no mater where it is located...
I knew there was an oil pump next to the rear end, but didn't remember if it was for the engine oil or the differential. Tried to find one of the cut-away car views, but it doesn't show it.
The more I think about it, the more I'm thinking it's under the hood. Otherwise, with the length of the oil lines to the rear, oil downs and fires would be far more prevalent.
Anyway, if the belt comes off, you lose oil pressure. Actually found the best info at Moroso. ;)