Yes, the sender can stick if it is worn out. I had one in my Valiant that had a broken spotweld that held the sender part to the tube in the tank and the whole works kind of bent over sideways in the tank. I just bent it back and soldered it in place. That tern plated (tin/lead) metal solders nice.
Another possibility is that your instrument cluster voltage regulator is bad. Does your temperature gauge work? Does it read normal or high?
If that voltage regulator goes bad and applies full voltage to the gauges then the gauges will read high or even burn out. I fixed an "overheating" problem on a Volaré for someone years ago by replacing their burnt out IC voltage regulator (they had the thermostat replaced 3 times in recent weeks trying to cure the "problem." Later I learned they had run out of gas because the gauge said 1/4 full and tank was empty. All this was caused by the IC voltage regulator not working.
Another possibility is if your pickup tube in the tank does not reach to the bottom or got bent. Or someone ran over something and dented the bottom of the fuel tank and pushed up the tube inside.
Now you have lots of things to check out...
