Freshening up Front and Rear suspension

Due to my negligence of suspension maintenance, this past weekend me and some buddies were left sitting on the side of the road. After getting out it was easy to what had happened as my rear wheel was facing the sky and the upper balljoint hanging out of its socket. So I thought while I was replacing this control arm/ ball joint I might as well do all four corners and make this thing as safe as I can since the parts are relatively cheap.

I've already ordered new upper control arms/ball joints for the front and lower ball joints for the front. And of course the upper control arms/joints for the read. My question is what about the lower joint/connection for the rear. I realize there is not a lower ball joint on the rear but what IS down there to hold it all together? Is it just the bushing? If it is, is it just a "inspect before you do anything" kinda of item? I just want to make it safe while not dumping a bunch of money into it.

Thanks

The rear lower suspension connections are just bushings. Definitely inspect them. If they are as old as your ball joints that broke, they probably need to be replaced.

You wouldn't happen to know the specific name of this bushing that parts store may have it under would you?

The bushing for the rear lower control arms is the rear lower control arm bushing. RockAuto has it.

There is also a rear lower shock/strut mount bushing for the bottom of the strut.