Negative thrust, as in enabling the helicopter to fly upside down...but no, the aerobatic Red Bull helicopter does not perform sustained inverted flight, it does barrel rolls and loops which maintain positive n.
Providing negative collective is not a design feature in helicopters. Ray Prouty briefly discusses sustained inverted flight in Helicopter Performance, Stability & Control, commenting on the extra collective travel required for negative collective pitch:
No actual helicopters are rigged in this manner, for two reasons. First, it would require a collective control system with twice the normal travel...Second, it would lose the important safety feature of having the down collective stop approximately corresponding to the right position for autorotation.
Upon a power failure, the collective needs to be lowered into the autorotation position within a couple of seconds, to prevent the rotor from loosinglosing RPM. With the collective down stop at correct autorotation position, the blade profiles must retain positive angle-of-attack, like in the pic below from the pretty good description on this site.
It seems that the autorotation setting at the collective down stop is a way more important design feature than negative thrust. Which would also bend the blades towards the tail boom, with possible catastrophic results.