Q.Can This Cactus Be Saved?
My niece was given this crafted cactus but told to water it only once every two to three months. The roots are still white and flexible, but the stem is hard and it does not appear to be absorbing water. Also, it appears that in order to fit into the tiny cup it was sold in the roots were cut off about half an inch below the barrel. Is there any way to save this? Either part of it? The top still appears alive, so if I cut it off and set it in soil would it root? I have not worked with cactus before, although I have worked with other grafted plants.

Certified GKH Gardening Expert
The host cactus appears dead, unfortunately. The top cactus (moon cactus) does not produce chlorophyll, and cannot survive on their own roots.
If you can find another Dragon Fruit cactus to graft them to, they will graft to it just fine.
Here are some articles that will help:
https://www.gardeningknowhow.com/ornamental/cacti-succulents/scgen/grafting-cactus-plants.htm
https://www.gardeningknowhow.com/ornamental/cacti-succulents/moon-cactus/care-of-moon-cactus.htm