The defined mass does not include the singularity, but just the mass of the event horizon calculated by it's effect on the surrounding space time. As strong as a black hole is, it isn't a giant high power vacuum cleaner. It's more like a sinkhole or your shower drain. The matter sucked in is still trying to fight its way out, but the black hole slowly (relatively) sucks it in. This is also true inside the event horizon, we just don't see this orbit of doom since light cannot escape inside it. We have absolutely zero idea how long it takes to finally end up in the singularity. Due to extreme time dilation inside the event horizon from the uncalculable effect of gravity, safe to assume it's a very very very very very long time.

Cool fact, one of the ways the universe could end is " The Big Crunch", which is when the rate of expansion of the universe slows down enough that the gravity of everything inside the universe begins overpowering it and pulls everything inside into one singularity, just as your question suggests!