The only part I have seen break on an 870 is the ejector and I suspect operator error in most cases. On some 870s, if you release the hammer with the barrel out of the gun, the hammer will slip behind the ejector. When you try to open the action again, the bolt snaps it off.
The other failure is the little tab on the ejector housing that positions the barrel. I have no idea as to how people break these, but they do.