That bar connects to the rear control arm and nobody seems to know what it's called. It broke off. What do I have to replace? The whole arm?

 

You have a "Delta Link" rear suspension. Two arms and an anti-roll bar. Each link is replaceable separately, have replace many left ones - they seem to get bent. If it's your anti-roll bar broken - that will make the car under steer more.

Volvo 850 rear suspension repair manual

 

Thanks that helped a ton. I found the mount online that broke. Hopefully that's the only damage. If anybody else has this issue, it's called the wishbone Anchorage mount