Slow down for a stop hitting the brake pedal, my back end will drop drastically?

Brakes problem
1991 Buick Century 6 cyl Automatic 91,000 miles

I've had my 1991 Buick Century for about 2 years now, and I noticed probably about a year ago, that when i'm driving and slow down for a stop hitting the brake pedal, my back end will drop drastically. It makes a loud thump noise, and kind of gives off what you would picture a lowrider car with hydraulics doing when it's back end drops. I've done it with people outside the car, and they say that can't physically see it dropping, but I know it does because I feel it. I would love to figure out what this problem is. Also, i've done it without actually going to a stop sign, and just doing it on my street, and it seems as though when I apply the brakes real quick it drops quick then when I release the brake pedal, it rises back up. So I know it ties in with the brakes somehow.