Part of a soap/ toiletries. toothbrush holder, from a ceramic washstand set. It may or may not have had a lid. Simple red/brown transfer-printed design to exterior.
Bone toothbrushes, bristles missing. (These would have decayed in the ground.) Toothbrushes were a luxury. Poorer people would have cleaned their teeth with a stick or marshmallow root or rag and soot.