Time does exist inside a black hole. Time exists for everyone, everywhere according to Einstein’s theory of gravity - General Relativity. What can happen is that you see time slow down and even stop for something else. For someone watching a black hole from the outside, nothing is ever seen to fall in, as anything that falls towards a black hole ends up frozen in time and compressed into an extremely thin layer at the event horizon. But this is not what is experienced by things that are actually falling. For them, time passes normally until they are destroyed by tidal forces. Nothing out of the ordinary happens for them at the event horizon.