  The interplay between unconventional Cooper pairing and quantum states
associated with atomic scale defects is a frontier of research with many open
questions. So far, only a few of the high-temperature superconductors allow
this intricate physics to be studied in a widely tunable way. We use scanning
tunneling microscopy (STM) to image the electronic impact of Co atoms on the
ground state of the LiFe$_{1-x}$Co$_x$As system. We observe that impurities
progressively suppress the global superconducting gap and introduce low energy
states near the gap edge, with the superconductivity remaining in the
strong-coupling limit. Unexpectedly, the fully opened gap evolves into a nodal
state before the Cooper pair coherence is fully destroyed. Our systematic
theoretical analysis shows that these new observations can be quantitatively
understood by the nonmagnetic Born-limit scattering effect in a s$\pm$-wave
superconductor, unveiling the driving force of the superconductor to metal
quantum phase transition.
