I saw some at a dealers. They had a stiff backing like tentex for the bodys and all the clothes had a lighter backing. With all the stiching, nothing showed through but was stable enough to support the designs and handleing of them. Also at the top of each clothing article she had a little tab to fold over to hold the clothes on.
Do you mean water soluble stabilizer? If so, unless it's meant to be free standing, you will end up with a pile of thread at some time!! Use something over that soluble stabilizer for the threads to hang onto!