Intermetallic compounds possess unique atomic arrangements that often lead to exceptional material properties, but their extreme brittleness usually causes fracture at a limited strain of less than 1% and prevents their practical use. Therefore, it is critical for them to exhibit either plasticity or some form of structural transition to absorb and release a sufficient amount of mechanical energy before failure occurs. This study reports that the ThCr2Si2-structured intermetallic compound (CaFe2As2) and a hybrid of its structure (CaKFe4As4) with 2 µm in diameter and 6 µm in height can exhibit superelasticity with strain up to 17% through a reversible, deformation-induced lattice collapse, leading to a modulus of resilience orders of magnitude higher than that of most engineering materials. Such superelasticity also can enable strain engineering, which refers to the modification of material properties through elastic strain. Density functional theory calculations and cryogenic nanomechanical tests predict that superconductivity in CaKFe4As4 could be turned on/off through the superelasticity process, before fracture occurs, even under uniaxial compression, which is the favorable switching loading mode in most engineering applications. Our results suggest that other members with the same crystal structure (more than 2500 intermetallic compounds) and substitution series based on them should be examined for the possibility of manifesting similar superelastic and strain-engineerable functional properties.