When i come to a stop my fuel gauge goes down to E and the car dies?

The car runs fine while driving and the gauge will read like 1/2 a tank or whatever its at and then as u slow down it drops till u come to a complete stop it reaches E and the car dies. What could be the problem? If you are stopped and the car is in park though it will idle fine and stay running for as long as you sit there but if u dont go as soon as u put it in drive it dies. It was doing this much worse, dying more often, untill we replaced a coolant sensor but that didnt fix the problem completly. This is in a 91 Saturn SC autotomatic 4 cyl. we had a test ran on it awhile back and they told us the fuel is running to rich. dunno if its connected with this problem or not.