From the late 19th cen on many types of composition furniture was made often from paper bases and sawdust even horse hair was used! with added resins and or glues. They were molded under high pressure by use of steam presses. A much less expensive way to make " carved" looking funiture.
You can repair them with a 2 part epoxy and clamping. Then sand the join and touch up the finish with acrilic paints The kind you can get at craft store as you'll need just a little of it. You could also drill both pieces and glue in some hard wood doweling as a repair. but the epoxy is easier to do.
hope this helps
Hallie in south fl.