You can handle it a number of ways. You can shut off the valve between the gas tank and the carb while the generator is running to run it out of gas. The gas left in the gas tank could benefit from the addition of a gas stabilizer while the generator is stored for the winter.
I like to have my generators available during the winter in case of a power outage at home. I put gas stabilizer in the the gas tank and run the generator for awhile to get the stabilizer into the carb. I use Sea Foam for a stabilizer. Others have had success with a number of other products.
If you don't take one of these approaches, you run the risk of gumming up the needle valve in the carb. which has an adverse effect on how the generator runs.