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Whatever you want to call it - you need one of these. With a lift, air tools and a spring compressor it can be replaced in about a 1/2 hour. Check the one on the other side - if you can turn the top nut (under the cap) with a wrench - it is torn also.
The seat in the picture is broken for sure. The one on the other side can't be too far behind.
If you do this yourself have the bearing plates standing by. These are the "lazy Susans" on which the strut pivots.
You can see the 3 nuts which hold the top of the strut in your picture. Those 3 studs are part of the bearing plate or mount.
While mine were in near new condition -unbelievable but true- some become heavily rusted. You remove them as part of the seat replacement job.
You can return them if you don't need them.
Here's a couple of pics. If your model is like the 850/V70, the spring seat is a molded hard rubber piece with a metal bush in the center that can tear free. the strut bearing as G noted is like a lazy susan. they don't break or wear out as often but given you need to open the strut to do the seat, it should be inspected for play and make sure it spins smoothly and replace if needed. I also have a pic of the mount for a S40 which uses a metal seat and a wonky bushing that can fail (particularly when the springs break). I suspect by your pic, your car is more like the 850s design but I'd need to look at a diagram (like those on the dealer web stores).
S40 Gen 1 strut mount 850/V70 strut with broken seat
In April 2019, I replaced all 4 of the 4C struts in my 2004 V70R. They were straight forward replacements EXCEPT for the rear passenger strut; the electrical plug for it to the wiring harness is WAY under the body, and it horribly difficult to unplug the old and plug in the new. I recommend cutting wires to the old one in the fender well and splicing in the new one. It had 126,000+ miles and drove like a new one after the replacement.