Thank you to all who shared ideas. Here's the scoop. The actual stiffening agent did, in fact, wash out with hot water and dish washing liquid. Around the edges of the piece it is mostly soft - as it should be.
However, in the middle, it is stiff - but not because of a stiffening agent, but from polyurethane, shellac, or varnish chemical reaction to the stiffening agent over time.
I'm going to take the piece to the dry-cleaners and see if they have any suggestions.
Thank you again for all your thoughtful responses. I truly appreciate them.
Janice