You might want to read up on how supernovae actually work...
Now, as I mentioned before, there are theories that predict
failed supernovae - check out
this paper for more details on that. In such a case, the star would spiral into the black hole with also no explosive signal.
On the other hand, the best understanding of gamma-ray bursts we have today tells us that massive stars can explode, producing a black hole
and a very powerful supernova at the same time.
Once the supernova explosion is actually launched (a process that obviously occurs but is still not really understood), there is no stopping the expansion.
Remember, black holes do not increase gravity!! If you have three solar masses within a radius x, this will have an (assuredly strong) surface gravity - if you collapse those three solar masses into a black hole the gravity at radius x remains unchanged!! Any matter that reaches escape velocity from three solar masses at radius x will escape from the black hole just as readily as from an uncollapsed core.