We study mechanical properties of polyelectrolyte multilayer microcapsules filled with polyelectrolyte solutions of high concentration. The osmotic pressure of counterions leads to a superswelling of microcapsules. The suppression of excess osmotic pressure causes a shrinking of capsules, which however do not return to their original, i.e., before swelling, size. To quantify these large and only partly reversible stretching of the shells, we develop a simple model, in which the stress-strain relation is constructed by mapping a linear model to two equilibrium, swollen and shrank, states. Fitting to predictions of this model shows that elastoplastic stretching of the multilayer is equivalent to a dramatic decrease in apparent Young's modulus, down to similar to 1 MPa in our experiment. This is in agreement with force-deformation profiles measured with the atomic force microscope, which show that superswollen capsules are ultrasoft.