A flying object can rotate around one of three axes defined as roll, pitch and yaw. Although the force on a haltere can be applied along all 3 axes, the measurement of that force is made by the two-dimensional stretch receptor at the base of the haltere. A single haltere has only two measuring axes. However, halteres are not positioned in a linear fashion and do not beat in parallel planes. They are typically offset by 120 degrees instead of 180 degrees. Thus, the halteres sense movements along two horizontal axes and two vertical axes. The separate signals from the two halteres are integrated in the fly nervous system to give roll, pitch and yaw information. The integration makes a fly more sensitive to changes in pitch than changes in roll.
A fly with one haltere can get some information on change in its flight attitude so it can still fly. A fly with no halteres is flying without sensors. The fly uses feedback from the halteres to make adjustments in body position that keep it airborne. Without information, the fly cannot prevent assuming unstable postures that cause it to fall through from the air.