Is it possible to fix a piece of furniture made of wood that got wet?

My mom took my furniture i got for my apartment and covered it with a tarp and duck tape and left it outside in our driveway close to the backyard because she didnt want it in the house (but didnt let me take it to my apartment right away either... i dont know why) Anyways, the tarp broke and the furniture got wet... show more My mom took my furniture i got for my apartment and covered it with a tarp and duck tape and left it outside in our driveway close to the backyard because she didnt want it in the house (but didnt let me take it to my apartment right away either... i dont know why)

Anyways, the tarp broke and the furniture got wet from the rain. The shelfs are still good, but the back kind of broke off and started rolling. My intention was to sand it and paint it. I am not sure i know how to fix this. The back was put on with nails i think. I saw nails in the back

This piece is made with wood. Are there ways to fix this? It looks like a china cabinet but doesnt have any doors on it.
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