Hello I'm Neal and I am here to help resolve your issue. If I cannot help I will opt out and refer your question to another expert.
What you were told was correct, but lacking in some detail. It is the sending unit which is part of the fuel pump assembly and to fix the problem, the entire assembly needs to be replaced. This will not cause the car to die or to break down. If you want to avoid spending the money to replace the assembly as it is pretty expensive, you can set your trip odometer to keep track of your mileage to help determine when you need to top the tank off.
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