Common sense would state that using a barrel tumbler for fragile fired clay parts would be inadvisable. The aggressive tumbling action would damage or crush the parts. This logic might follow for brittle parts such as ceramic tile and the like.
In fact, tumbling all types of fragile and brittle parts can be accomplished quite successfully in a barrel tumbler. The part in the picture above is a molded and fired clay pendant that is only about 1/8″ thick. The project required that the excess material on the edges be removed and that the edges are heavily rounded.
In this case, a wet process would have involved undesirable absorption of water into the pendant. A dry tumbling process was used to achieve the stated goals. The parts were tumbled with Hardwood Tumbling Media Media and White Aluminum Oxide Grit for less than 2 hours to achieve the edge rounding as seen in the part on the right. As long as the proper ratio of media to parts (about 4:1 in this case) is maintained, damage the parts will be insignificant and batches as large the barrel will allow can be done.