The unwinding of the compact, partially collapsed chains at their elongations is studied by Monte Carlo (MC) simulations. The stretching of single chains below the theta point is described by elastic functions exhibiting region of mechanical instability specified by a concave curvature of the elastic free energy and a van der Waals loop in the reduced force. The elastic free energy and the stress-strain isotherms of supercoiled networks of the c* gel type formed by collapsed chains were evaluated by the three-chain model. The stress-strain isotherms exhibit a long plateau with a low elastic modulus and high ultimate drawing ratio (i.e., characteristics of the superelastic behavior outlined previously in deswollen networks). A substantial difference in the elastic response was found between supercoiled networks and ordinary melt-crosslinked networks. The instability region was observed on some computed stress-strain isotherms of supercoiled networks, indicating the two-phase structure of a network, a phenomenon relevant also in the biopolymer gels having compact structures which unwind on stretching.