  The physical nature of Fast Radio Bursts (FRBs), a new type of cosmological
transients discovered recently, is not known. It has been suggested that FRBs
can be produced when a spinning supra-massive neutron star loses centrifugal
support and collapses to a black hole. Here we suggest that such implosions can
happen in supra-massive neutron stars shortly (hundreds to thousands of
seconds) after their births, and an observational signature of such implosions
may have been observed in the X-ray afterglows of some long and short gamma-ray
bursts (GRBs). Within this picture, a small fraction of FRBs would be
physically connected to GRBs. We discuss possible multi-wavelength
electromagnetic signals and gravitational wave signals that might be associated
with FRBs, and propose an observational campaign to unveil the physical nature
of FRBs. In particular, we strongly encourage a rapid radio follow-up
observation of GRBs starting from 100 s after GRB triggers.
