My 93 Buick Park Ave. shuts off randomly when driving.

Your car is designed to run like a well-oiled machine, but sometimes that machine struggles in unexpected places. There’s not always a warning light to alert you of this, but sometimes your car will be driving fine at road speed, only to die when you slow down and stop. If your engine shuts off at low speed, contact a mechanic immediately for a thorough inspection.
Common reasons for this to happen:
Malfunctioning transmission
Low fuel pressure, dirty or defective fuel injectors, or broken fuel pump
Bad oxygen sensor or mass flow sensor
Loose or corroded wires in wiring harness
Faulty idle air control actuator
Clogged or restricted EGR Valve.

You will need a flashlight; it will be very helpful. Standing on the passenger side of the vehicle, shine the flashlight down behind the engine approximately in the corner behind the pulleys but a little more closer to the firewall and look straight down. The power steering reservoir sits like one to two feet below where you probably expect to see it; they seem to have hidden it very well . I have a 98 and a 99 Park Ave and it took me forever to find it.

Remove starter and take to Auto zone,they will test for free,takes just a few minutes,here's how to remove.Here's where the starter relay is.

my 1st guess wd. be crank sensor

When was last "healthy" tune up? Plugs, wires, ALL filters including FUEL filter? I'd start there, and run a good fuel system cleaner w/next tank full of fuel. In winter, with fluctuating temps, condensation (water) forms in fuel tank and spark plugs don't burn fuel/water efficiently causing stumbling and premature wear on your plugs.

Try replacing your throttle position sensora(TPS). Had the same problem with my 93 park avenue.

Fuel pump ?

Good luck !

sounds like a battery terminal ,or earth connection from battery to chassis ,or where the power is picked up from which is the starter motor terminal ,sorry i am not very explicit but i live in spain and not may buicks to the euro here,But if i got my greasy hands under the bonnet i could no doubt find the problem

replace the crankshaft poistion sensor

Put a crank sensor on it to fix.