From the way you word your question, I gather you are thinking of a black hole in terms of the 'frozen star' picture common in early theory. Things fall 'onto' the event horizon, but as time slows down there, they get slower and slower, the light more red-shifted, and never reach it.
This isn't what actually happens. To explain what is going on, here is a picture of a black hole, using a special coordinate system (Kruskal-Szekeres coordinates) that twists round to keep the lightcones aligned. Tilt your head $45^{\circ}$ to the right to see the usual 'spherical object with a singularity in the middle sitting in space' picture. Time experienced by a local observer goes up the page, space goes horizontally, lightspeed is shown by lines at $45^{\circ}$. (Bear in mind that time differences and distances are distorted, we've crammed a curved 4D spacetime into a flat 2D picture, and you should therefore be careful not to take it too literally.)
What any point in spacetime 'sees' directly towards or away from the black hole can be determined by looking along the two $45^{\circ}$ lines pointing down the page. These are called the past lightcone at the point.
An observer hovering at a constant distance outside the black hole travels along the hyperbola shown on the right. They see the light of the collapsing star that fell into the hole millions of years ago, still struggling up out of the gravity well. The longer the time, the more oblique the angle and the slower (more red-shifted) the emissions seem to be, but the process never stops. No matter how far up the page you go, the hovering observer can still see the light from everything that has fallen in in the past. This continues long after the objects have hit the singularity and ceased to exist. (Although times are not really comparable as being 'before' and 'after' one another when separated by an event horizon like this.)
For a falling observer, their past lightcone rapidly approaches and crosses the event horizon, and their view of the past is no longer being redshifted as much. They see the collapsing star pass through the event horizon and head rapidly towards the singularity. But the falling observer hits the singularity themselves before they see the star's matter complete its journey.
The singularity is twisted round so instead of being timelike it is now spacelike. So as seen in the diagram, the collapsing star and the observer hit it at different now-spatial positions along it. The time experienced by either between crossing the event horizon and hitting the singularity is roughly the same. If the star fell in millions of years earlier, its clock would show the much earlier time.
This assumes an idealised theoretical Schwarzchild black hole, where the infalling mass is assumed to have no gravity itself. The true picture in a more realistic Belinsky-Khalatnikov-Lifshitz model has the spacetime stretching and oscillating chaotically as the masses approach the singularity. But the above discussion should be accurate enough to undertand what's going on outside and near the horizon.
