  We consider the limit of solutions of scaled linear kinetic equations with a
reflection-transmission-absorption condition at the interface. Both the
coefficient describing the probability of absorption and the scattering kernel
degenerate. We prove that the long-time, large-space limit is the unique
solution of a version of the fractional in space heat equation that corresponds
to the Kolmogorov equation for a symmetric stable process, which is reflected,
or transmitted while crossing the interface and is killed upon the first
hitting of the interface. The results of the paper are related to the work in
[KOR20], where the case of a non-degenerate probability of absorption has been
considered.
