Can we see dead stars with the naked eye?
When a star dies. (By that I mean when there are no more nuclear fision reactions going on in it), it can take three different forms. Depending on the initial mass of the star, it will become either a white dwarf, a neutron star or a black hole.
You can immediately
rule out seeing black holes because they don't emit any light, and neutron stars becasue they are too small. This leaves us with white dwarfs, which are the larger of the three possible end products for stars.
Unfornately, you will not be able to see even the brightest white dwarf. Astronomers describe the brightness of stars by their magnitude. The magnitude scale goes backwards such that a star with a magnitude of 4 is fainter than a star with magnitude with 1. With the naked eye and a clear sky, you can see stars about up to magnitude 6, and it turns out that the brightest white dwarf has a magnitude of 8.3.
Moreover, that the brightest white dwarf is in a binary system: it is the companion of the brightest star in the night sky: Sirius (that star is called Sirius A and its white dwarf companion is Sirius B). This makes it even more difficult to see, since the light from Sirius A overwhelmes that from Siruis B. But still, you can look at Sirius and imagine you are looking at two stars, one of which is a white dwarf!
The other idea would be to look at other remanants of stars: planetary nubulae. When a star dies and becomes a white dwarf, it ejects some gas into space that appears to glow because it is illuminated by the stars. If you can see a planetary nubulae, it means that there is a white dwarf in the centre of it. But once again we fall out of luck, since the brightest planetary nubula, the dumbbell nubula, has a magnitude of 7.4, which means you cannot see it with the naked eye.
What are Black Holes?
Black holes are the result of a gravitational collaspe that distorts the
fabric of spacetime so drastically, nothing (save radiation) is allowed to escape. The formation of black holes is driectly linked to the life cycle of a star. Eventually, stars
exhaust their nuclear
fuel, and are no longer able to counteract the inward pull of gravity. The
core of the star collapses, making it very difficult for that star's light to escape the core's tremendous gravitational pull. The star eventually passes through what is called an event horizon (a cosmological point of no return) and forms what is called a singularity, a
single point of infinate density.
Can We See Black Holes?
Because light cannot escape the gravitational pull of a black hole, it is impossible to see those objects with the naked eye. There is a good amount of evidence that suggest they exist. Perhaps the most convincing (outside of our cosmological models, which are evidence enough for some, myself included). Photgraphs taken with different renderings, such as infra-red, that can see gasseous movements that our own naked eye cannot.
What Happens if Something Falls into a Black Hole?
Because we have never physically seen anything falling into a black hole, and because even if we were to see something fall past the event horizon, we would no longer be able to view it (remember, light cannot escape) we can only theorize about what would happen if something were to fall into one.
Because we know that the gravity in a black hole is so strong that light even even cannot escape, the common theory is that something will slowly be crushed into a compact singularity over time. Of course, the likeihood of something falling into a black hole seems likely
remote. Certainly you and I have nothing to worry about. There have not been any black holes detected anywhere in our vicinity. There is, however, the very likely possibilty that there is a black hole much closer to us that most would imagine.