Answer
The half of the satellite that momentarily stops will fall vertically straight downward to Earth. Using conservation of linear momentum, we conclude that the other half will attain twice the satellite's original velocity.
$$ Mv = (\frac{M}{2})(0) + (\frac{M}{2})(2v)$$
It will move farther from Earth.
A more quantitative analysis shows that twice the orbital speed will exceed the escape speed of Earth, so the second piece will escape Earth's gravity and fly into the wild blue (black) yonder.
