Answer
She increases her moment of inertia.
Work Step by Step
By extending her arms straight out to the sides, she moves mass farther from the axis of rotation (the wire). That means that for a given unbalanced torque, the angular acceleration will be relatively small, because the moment of inertia is larger.
$$\Sigma \tau = I\alpha$$
$$\alpha = \frac{\Sigma \tau }{I}$$
With a smaller angular acceleration, she won’t rotate as far in a given time, giving her more time to “catch” herself and straighten up.
