What happens to the radiation already in progress when blackhole gobbles up lot of material nearby?

Let us consider an event of a blackhole gobbling up a large amount of material nearby when radiation was in progress from a source just outside its blackhole boundary. Let us further assume that this causes the blackhole boundary to expand so that the source now finds itself within the blackhole boundary. The question is: now what happens to the radiation from the source that was already in progress outward away from the gravitational center?