In order for a helicopter to maintain a straight and level flight or hover upside down, it needs to reverse the thrust of its main rotor.
There are some radio controlled helicopters capable of doing that (the trick is also known as the "lawn mower"), but not real helicopter can do that.
However, some real helicopters (not remote controlled) are capable of performing loops and rolls. This is usually done only by aerobatics pilots and is considered to be a dangerous maneuver. During a loop, the helicopter's thrust is not reversed and the whole airframe is under positive G factor (unlike a stable upside down flight which put the airframe under negative G factor).
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