  We consider a situation where a light source orbiting the innermost stable
circular orbit (ISCO) of the Kerr black hole is gently falling from the
marginally stable orbit due to an infinitesimal perturbation. Assuming that the
light source emits photons isotropically, we show that the last radius at which
more than 50\% of emitted photons can escape to infinity is approximately
halfway between the ISCO radius and the event horizon radius. To evaluate them,
we determine emitter orbits from the vicinity of the ISCO, which are uniquely
specified for each black hole spin, and identify the conditions for a photon to
escape from any point on the equatorial plane of the Kerr spacetime to infinity
by specifying regions in the two-dimensional photon impact parameter space
completely. We further show that the proper motion of the emitter affects the
photon escape probability and blueshifts the energy of emitted photons.
