If I throw a clock towards a black hole, its time slows down, it is redshifted, and according to many theories it never reaches the event horizon from my point of view. How is it then, that a star can fall into a black hole, and be observed to do so by me (by its emission of gravitational waves)?
The LIGO results are about the merging of two black holes, and gravitational waves are expected mathematically to be emitted due to the great distortions of space as the two massive black holes merge. One has to remember it is general relativity at work here.
Something similar will happen when a star is absorbed, again space distortions will be great. A clock falling into a black hole distorts space in so tiny a quantity, due to the small gravitational constant its mass is insignificant with respect to the black hole mass, that any gravitational waves of its disappearance ( or not depending on the observer) cannot be recorded. It took the order of sun masses size of the two merging black holes to be detected by LIGO.