Pat,
My home course, Washington Golf & Country Club, was designed by Donald Ross and it contains the feature you write about.
Behind the par 4 8th green, there is a sharp slope running away to a creek about 25 yards behind the green. About a third of the way down, there is a containment backstop built into the main slope. It is obviously meant to prevent balls from bounding over the green and running into the creek.
Personally, I am not a fan of this feature, as it built too sharply into the downslope, creating something that looks kind of like a grass bunker with a triangular bottom. In addition, it drains poorly. I'm not an expert, but it looks like it blocks the flow of water down the hill, causing water to pool at the angle between the backstop and the hill.
It's possible that this backstop was added because of the nature of the approach. The green looks as if it was originally meant to (and still does) accept a running approach-the green is open at front and slopes away from the fairway. Maybe Ross (or whoever added the backstop) felt that a ball running just over the green and into a creek would be too harsh of a penalty considering the inexact, sometimes unpredictable nature of a running approach. Thus the secondary backstop.
Pat, thinking along those lines, are the holes that you reference ones that require running approaches (long par 3s, short par 5s?) with steep downslopes, or other hazards, behind the green?