When the fuel gets low enough, there is also the potential to uncover the fuel inlets during maneuvering - not likely but possible. And yes, it has happened - I'm going to say mid 1980s (but stand to be corrected), 747 on a short positioning flight took off with minimal fuel on-board. Being very light, they climbed at a high angle and two engines flamed out due to fuel starvation when the fuel inlets were uncovered at the high AOA.