The anomalous responses of electrospun nanofibers and film fabricated of unfolded bovine serum albumin (BSA) under constant stress (creep) is observed. In contrast to typical creep behavior of viscoelastic materials demonstrating (after immediate elastic response) a time-dependent elongation, in case of low applied stresses (<1 MPa) the immediate elastic response of BSA samples is followed by gradual contraction up to 2%. Under higher stresses (2-6 MPa) the contraction phase changes into elongation; and in case of stresses above 7 MPa only elongation was observed, with no initial contraction. The anomalous creep behavior was not observed when the BSA samples were subjected to additional creep cycles independently on the stress level. The above anomaly, which was not observed before either for viscoelastic solids or for polymers, is related to specific protein features, namely, to the ability to fold. We hypothesize that the phenomenon is caused by folding of BSA macromolecules into dry molten globule states, feasible after cross-linked bonds break up, resulting from the applied external force.