Clay doesn't have to be the main thing in a piece of artwork. Some time ago, I tried making frames for some two-dimensional work I had done. I made the first small picture in a class-setting dealing with tile and slab-rolled clay. It is a quick watercolor sketch I made in Hawaii.
Constructing of the first frame includes creating a small raised frame in the back of the piece to accommodate the glass, the work and a backing. This piece has only tape holding the backing on, since it is a very small and lightweight. A peak similar to the one on the front located at the center top is repeated on the back to provide a hanging place using a small nail. In the place of tape on a larger work, holes could be made in the clay and, after firing, small nails or mounting triangles could secure the backing. Some expeimenting would need to be done to account for shrinkage.
The second sketch was done in Guam and is an abstraction of an incredible panorama of beach, headland and surf that could be seen from the crest of a road. It is from memory. I painted it as if viewed from a window with a curtain of fabric drawn back. It's called "Room with a View".
In this case, I built into the design a way of hanging the work by extending the frame, making holes in the extensions, threading and anchoring the multiple threads with knots at the bottom. It is also unglazed on the back and sealed with tape. This method of hanging opens all kinds of possibilities for interesting materials that become part of the design relating to the frame or the work it contains: Cording, leather, wire, rope, wood, reed, etc.