To raise the superconducting-transition temperature (Tc) has been the driving force for the long, sustained effort in superconductivity research. Recent progress in hydrides with Tcs up to 287 K under 267 GPa has heralded a new era of room-temperature superconductivity (RTS) with immense technological promise. Indeed, RTS has lifted the temperature barrier for the ubiquitous application of superconductivity. Unfortunately, formidable pressure is required to attain such high Tcs. The most effective relief to this impasse is to remove the pressure needed while retaining the pressure-induced Tc without pressure. Here we show such a possibility in the pure and doped high-temperature superconductor (HTS) FeSe by retaining, at ambient via pressure-quenching (PQ), its Tc up to 37 K (quadrupling that of a pristine FeSe) and other pressure-induced phases. We have also observed that some phases remain stable without pressure at up to 300 K and for at least 7 days. The observations are in qualitative agreement with our ab initio simulations using the solid-state nudged elastic band (SSNEB) method. We strongly believe that the PQ technique developed here can be adapted to the RTS hydrides and other materials of value with minimal effort.