No Gas to the Carb When Engine Warms Up

Here's a true story...... I had a friend who had a car that he drove everywhere. One day as he was driving along the car started slowing down and finally died. He would have to wait a few minutes then it would start again and run real good but then later on it would start slowing down until it died again. He had a good idea that it was engine was running out of gas but didn't know why. He drove the car like that for months trying different things to fix it, fuel pump, fuel filter, gas cap, carb filter. One day he got really pissed off and pulled the gas tank. He found that someone had stuffed a shop rag down into the tank. The rag would float around until the pick-up sucked it up. Once the engine died the rag would float away and he could drive again. I'm not saying that you have this same problem:
If you turn the engine off for a few minutes then restart does the fuel filter get full again??

Treblig