What a brilliant idea! I love it. Thanks for the information.
The soap molecules in the water only slightly remain in among the water molecules that pack together to form crystals as they freeze. Most of the soap remains in the liquid water between the crystals. In the end one is left with the original crystals of nearly pure water, surrounded by weaker crystals that contain some soap, surrounded in turn by the concentrated residues of soap that remain as a grease-like, spongy structure, preventing the ice crystals from joining up into a hard, brittle mass.
The traces of soap within the crystals affect their growth during freezing, making them more branched and delicate, and accordingly, less able to form a rigid, brittle structure.
Frozen custard behaves in much the same way, though I have never tried it in a trumpet (finger trouble, possibly Freudian, made me type strumpet, but I have no experience of mitigating their hardness when frigid, promise!)
The overall effect is to make the crystals more prone to slide past each other with reduced resistance, or for planes of water molecules to slide past each other without breaking the crystal.
Such a material is more putty-like than pure ice, more malleable as you put it. You might like to think of it as a sort of stiff slush. However, although filling and sealing the trumpet and trying to bend it with nothing more than liquid water inside, would maintain a constant volume, it would not perfectly prevent kinking. The solid mass of soap-and-water "putty" does have enough strength to circumvent that problem.
Altogether charming. I wonder which unsung genius thought of it, and when he did so. I also wonder whether he did not get beaten up by his colleagues for his cheek in ruining a traditional skill of bugle bending. Presumably it is a recent development, because artificial refrigeration as a routine technology is less than two centuries old, though trumpets, I believe, are more like two millennia old.
Humph! I have just been surfing the web and it seems that the soapy water is at least not a generally used filler, or if it is, then manufacturers are secretive about it. Few sites mention the tube bending process, and those that I found spoke of filling the tube with soft metal that had to be melted out at the end of the process.
No matter, I loved the question!
I wonder how many other tube-bending dodges people have come up with over the years...
Jon