Fixed wing aircraft can fly with fewer than all engines because the engines only provide thrust, not lift or aerodynamic stability. With multicopters the propellers are the wings, and while it's not completely analogous to expecting a fixed-wing aircraft to fly with only one wing, the problem is similar. In principle a quad can fly with just three rotors, with primary lift being provided by the two remaining diagonally opposed can counter-spinning rotors and rotation around the axis connecting them being controlled by the third motor. That's unbalanced in terms of angular momentum around the vertical axis, leading to a lack of yaw control (you can live with that), but it also likely requires the third motor to be reversible in order to be able to provide up or down thrust.