The normal presentation of these gravitational time dilation effects
can lead one to a mistaken conclusion. It is true that if an observer
(A) is stationary near the event horizon of a black hole, and a second
observer (B) is stationary at great distance from the event horizon,
then B will see A's clock to be ticking slow, and A will see B's clock
to be ticking fast. But if A falls down toward the event horizon
(eventually crossing it) while B remains stationary, then what each
sees is not as straight forward as the above situation suggests. As B
sees things: A falls toward the event horizon, photons from A take
longer and longer to climb out of the "gravtiational well" leading to
the apparent slowing down of A's clock as seen by B, and when A is at
the horizon, any photon emitted by A's clock takes (formally) an
infinite time to get out to B. Imagine that each person's clock emits
one photon for each tick of the clock, to make it easy to think about.
Thus, A appears to freeze, as seen by B, just as you say. However, A
has crossed the event horizon! It is only an illusion (literally an
"optical" illusion) that makes B think A never crosses the horizon.
As A sees things: A falls, and crosses the horizon (in perhaps a very
short time). A sees B's clock emitting photons, but A is rushing away
from B, and so never gets to collect more than a finite number of
those photons before crossing the event horizon. (If you wish, you can
think of this as due to a cancellation of the gravitational time
dilation by a doppler effect --- due to the motion of A away from B).
After crossing the event horizon, the photons coming in from above are
not easily sorted out by origin, so A cannot figure out how B's clock
continued to tick.
A finite number of photons were emitted by A before A crossed the
horizon, and a finite number of photons were emitted by B (and
collected by A) before A crossed the horizon.
You might ask What if A were to be lowered ever so slowly toward the
event horizon? Yes, then the doppler effect would not come into play,
UNTIL, at some practical limit, A got too close to the horizon and
would not be able to keep from falling in. Then A would only see a
finite total of photons form B (but now a larger number --- covering
more of B's time). Of course, if A "hung on" long enough before
actually falling in, then A might see the future course of the
Bottom line: simply falling into a black hole won't give you a view of
the entire future of the universe. Black holes can exist without being
part of the final big crunch, and matter can fall into black holes.
For a very nice discussion of black holes for non-scientists, see Kip
Thorne's book: Black Holes and Time Warps.
From this source