Yes, although the pics are small I can tell by the shock end. You have the same bumpers I do. Basically, there were two right angle tabs inside the bumper that the big rubber covered end of those shocks slid into, top and bottom. Then it was bolted to the car. Your tabs are gone and it's a common problem with rear bumpers. Your shocks look OK, but you'll need a new bumper. The salvage yard near me doesn't have that style so I can't help you out with a replacement. An alternative I have seen before involves removing the impact strip, drilling four holes (that will be covered when impact strip is reattached) through the bumper and the shock end, and using the flattest pan head stainless steel sheet metal screws you can find to basically screw the bumper onto the shock. When you put the impact strip back on, you can't see the screw heads, but depending on their head hight, they may push the strip out a bit. I have thought about how I would fix this if I needed to, and I don't yet, but if I did I would do this: I'd have a new brackets fabricated with using a piece of 1/4" aluminum c-channel and 2 pieces of 1/4" flatbar. I would put them on the end of the shocks. Then, I would drill 4 5/16" holes through the bumper at the same points the screws would have been, over where the shock ends would be, under the impact strip. I'd drive to a welding shop, put the rear bumper in position, and have it plug welded to the the new brackets which are on the end of the shock. This would be a real fix, the shocks would be able to be replaced, the bumper is permanently attached to the new brackets, and there is nothing sticking up to interfere with the impact strip. I don't know if this has ever been done, but I think the theory is good. Below is a crude diagram, with the light gray piece being the piece I'd have made and the red dots the plug welds.
