The escape velocity from any orbit about the Earth is given by
2 2 G M
V = -----------
R
But the circular velocity of a body in a stable orbit is just
2 G M
V = ------------
R
This means that if the Earth suddenly lost 1/2 of its mass, the
circular velocity it once had BEFORE the change, would now equal the escape
velocity, and so the satellite would escape. If the Earth only lost 1/4
of its mass, the Moon would go into a highly elliptical orbit whose
perigee distance would be about equal to its current average velocity in its
orbit. Its apogee distance would probably increase by a factor of two or so
from its current mean distance. But you would have to consult a textbook
on celestial mechanics to get the correct new orbit parameters.