This was how the BMW i3 worked. It was a rather novel design that included an optional small electric scooter motor in the rear that had a 2.5 gallon gas tank. When the battery was low, it would be charged by running the small generator.

This was clearly a wonderful idea but it was hamstrung by a silly California rule requiring the gas range to be less than the electric range to qualify for rebates. With a 6 gallon tank, the car would have been able to do ~300 miles instead of 170 and would have been parked in everyone’s driveway.

An added benefit was that the car could use existing gas station infrastructure when you needed to travel long distances.