On a helicopter, the collective is used to adjust the attack angle of all the main-rotor blades in the same direction by the same amount, causing the amount of lift generated to increase or decrease symmetrically across the whole main rotor, which, in turn, causes the helicopter to climb or descend. If the collective is pulled all the way down to zero, the main-rotor blades move to zero attack, generating no lift (this is useful when on the ground).
Negative collective, if possible, would cause the main-rotor blades to move to a negative pitch, causing them to generate negative lift and accelerate the helicopter downwards. This would enable a very rapid descent, which could be useful in certain circumstances (for instance, in combat). Can any helicopters actually do this?