Modern fighter planes are inherently unstable because this is required for better maneuverability. Passenger planes can certainly benefit from that too.
Consider gusty crosswinds during a landing. With an inherently unstable aircraft, there is greater capability to compensate. You can have a computer stabilize the plane, preventing the tail or wing tips from striking the ground. When wake turbulence threatens to flip the plane or when a microburst threatens to pound the aircraft into the ground, a fast response is possible. Stability would deaden the performance of the needed response.
The extreme example is probably wings that are low-mounted anhedral and forward-swept, with the bending controlled by rapidly actuated aerodynamic surfaces near the tips.