What is it?

I have a 1989 5.0 mustang I am trying to get back on the road after it has sat for many years. Change all the fluids replace what looks worn out filters the works so I am looking at the rear suspension and don't know what this part is so I can look for a new one or at least know what it does. I hate to look like a noob for asking this question but if you look for suspension parts which there is about a million or more out there I have not come across one of these to even know the name of it. It looks to be a factory part, there is one on each side. Here is a picture, caution there may have been spiders killed to take this photo

Thanks! I think they even miss label this part lol. Lists as a stabilizer but is more of a damper than a stabilizer. I don't see where it would do much good unless the control arms are sloppy or the mounts where spot welded out of place. My mustang is an automatic so I am going to try some better control arms and leave em off and see how it does. I already have the weld in sub frame connectors on the way.