Unlike other plants, cactus have no built in shut off valve. It will absorb every drop of water it gets. The interaction between the roots and the top to supply/build the nutrients needed by both systems is a balancing act. Right now, your plant's balancing act is not balanced.
There's no chlorophyll in the white half so the green half has to support the whole top. The roots are not helping right now. The green side is supporting the entire plant and its having to use stored reserves to do it. If it were mine, I would plunk that puppy down on some damp cactus soil and stick it in a shady spot. Water sparingly until the roots grow.
Daisy