A black hole definitely absorb matter but for an observer outside the black hole at some point nothing would move and eventually we would see matter freeze in time before the event horizon forever. For the matter falling into the black hole the story is different. It would fall and time dilation would become so strong that space-time would actually make it that time would stretch into the future in relation to us on earth for example. In other words, space-time falling into a black hole as it gets closer to the event horizon is billions of years into the future…I still can’t get my mind over it but it’s what time dilation is. And a black hole is made of a singularity, the event horizon, capable of basically sucking the fabric of space-time with its enormous gravity attraction. When scientists try to calculate the power of gravity inside the black hole they end up with infinity, hence the term singularity used to define the event horizon. It’s pretty incredible and quite fascinating that the universe itself is capable of that. I would highly recommend the book about black holes by Leonard Susskind. He is the reference when it comes to understanding the phenomena of such monstrous celestial beast. All the best.