I have bolts of fabric that have been stored on the original cardboard bolt for years. In fact I just rediscovered a partial bolt of muslin that I had for 20 years. There was no damage to the fabric from the bolt.
I reuse my bolt cardboard to store other large pieces of fabric. Sometimes I just cut down the original bolt. When ever I purchase a large piece and it is the end of the bolt , I request that they wind it back on the bolt. Additionally , I request empty bolts from my LQS and have never had them say no to my request. But thats just me and my exerience. I just hate to purchase something special when a viable option is free and reuses something that would be discarded.