I am not getting any shock action on the rear of my 2000 Lesabre. The rear of the car gets unstable when hitting bumps; like driving a hardtail. The problem came on suddenly after not driving it for about a month.

Ok first of all your car has shocks in the rear and they are not very hard to replace or terribly expensive. The front has what they call struts which in effect are shocks with a springs wrapped around them as an assembly. Replacing struts can be expensive and will probably need to be changed by a shop if you are not equipped to do it yourself. You will most likely need to get the wheels aligned as well. I recommend calling around to different shops for a price. My guess for new front struts installed plus the alignment is $300-$400.

If the bouncing is in the front it is probably a strut.
If the bouncing is in the rear it is probably a shock
look for the shock to be oily indicating the shock is bad. But
usually if the car is bouncing two or three time after hitting a bump
the shock has either broken or come completely loose.

If you have fitted new shockys I suggest you check the travel of the units as it sounds as if they are bottoming out Pistons hitting bottom of internal cylinder.

Sounds like you have a bad or broken shock or strut in back. Have mechanic check for this.

are they adjustable shocks

worn suspension shocks sway bar broke bring to local mechanic and have inspected

That is a sign that your rear shock absorbers a shot

Sounds like shocks are worn out. Test by bouncing car by hand. If it continues to bounce after you stop they are bad. It is best to replace front and rear both. Also many front wheel drive cars have struts on front instead of shocks. If you have a garage fix it, tell them the symptoms, so they can properly diagnose.

the rear shocks are worn out check and replace also check the u-joints in the drive axles

it should be air adjustable, if the pump is working, most of the time the shocks leak. have a shop ck out the rear shocks, if they leak, then verify that the pump is operational. Monroe offers replacements.