Many GM gas gauges are notorious for this, especially if the owner(s) have used lesser grade fuels. The windings on the sensor will often corrode and as a result, there will be no contact with the wiper. Not sure about the STS but often this requires replacing the entire fuel pump as they are part of a single assembly. There are some additives (available from GM) that will sometimes correct this but they are usually a limited time cure.
There are of course other possibilities for this problem as well.