I have a 1991 Pontiac Grand Prix that will shut off when coming to a stop or slowing down.

Sounds like an ignition coil issue

Unfortunately, yes. It's a pain. I own a 1991 Pontiac grand prix SE 3.1L.

My fuel pump problem started when I ran out of gas (gas gauge was offset) Of course it shuts off w/o gas but it will more likely kill your fuel pump and clog the $#!t out of your filter.

If it makes a buzzing sound under the vehicle w/o the engine running, near the trunk area, replace it along with the filter.

There are SO many things that could be to blame, such as a relay sticking in the Engine Management System, which controls fuel cut-off on deceleration, for example.

Have you changed the fuel filter yet?
If it's the original on a 99 model and a previous owner has run the tank dry, it will have sucked dirt into the filter.

Otherwise, the fuel pump may not be working efficiently.
Does the engine sound ok and maintain steady revs, around 850/900rpm when it's started up?

Disconnect your negitive battery cable,go under car and remove any brackets on your starter,then the 2larger bolts that hold it to the block,lower it down and remove wires.

possible bent linkage or the turn key needs replacing due to wear over time and use

This is a known issue for your model and for GrandAm's. Best to take it to your dealer.

Clean or replace the idle air control valve.

The best solution is to do a complete tune up with new spark plugs, wires, fuel filter, air filter, pcv valve and oil change.. If this still happen I would get some fuel injector cleaner, or use marvel mystery oil in both your oil(crankcase) and gas tank. You can get mystery oil at walmart..its in a red bottle with black label.

Try checking the starter solenoid wires.Make sure the wire hasnt come loose and the battery to solenoid cable is tight.

check your relay and underhood fuse pane to see if you pinced some wiring