I have been reading the Ender quartet and was wondering if the Descolada, a disease introduced in The Speaker for the Dead, was based on a disease in the real world. Is there a virus that goes around in the body changing random genes until the body entirely rejects itself and dies?
No. The Descolada's pathology makes no sense for a real-world virus.
First of all, "changing random genes" would result in death from all the infected cells dying in the body long before an immune response would become relevant. In general the biological description of the Descolada's symptoms and methods of action is questionable at best. It's effective sci-fi, but in reality exposure to mutagens doesn't make people grow new limbs (although it may produce such effects in their children). Besides, changing DNA so dramatically would run contrary to the virus's own reproduction and evolutionary success.
Believe it or not, super-lethal viruses are actually selected against in evolution because they kill their hosts too quickly for them to spread effectively. Viruses need to infect a host cell in order to reproduce, so killing their host leaves them out in the cold. The 1918 Spanish flu is a good example: no one ever developed a cure, the virus just killed people faster than it could spread to uninfected populations. Over time, viruses typically evolve to be less lethal to their hosts, not more, because it gives them more opportunities to spread and removes evolutionary pressure for the immune system to fight them. Arguably, the most successful viruses of all are those that that made total peace with the species they infect: each of our genomes is about 10% virus, the relics of ancient infectors who found that it was more efficient to just stay dormant inside human cells than it was to go through the bother of waging infection.
So it makes sense that an alien virus, poorly adapted to infecting humans, would absolutely destroy their biology. This is similar to what happened with HIV, which spread to humans (where it's a serious illness) from chimpanzees (where its counterpart, SIV, is completely harmless). But any virus as fatal as the Descolada couldn't last for long: it would wipe out its own pool of potential hosts, to its own detriment.
Viruses can however alter their hosts' DNA. Some viruses, called retroviruses, insert their own genomes into the host cells' genomes (HIV is an examples of this), while others, called oncoviruses, can produce cancer-causing mutations. So I think the closest you'll ever get to the Descolada you'll find in real life would be something like HPV, most notorious for being a cause of cervical cancer.
There is also some evidence that certain bacteria can cause cancer, but this is not as well established as it is for viruses.
If we forget about mutating the host's DNA and focus solely on the immune response, then maybe we can get a little closer. There are many viruses that kill not by the direct effect of their infection, but by provoking an immune response so intense that the body is killed by its own defenses. This isn't a case of immune "rejection" (the body detecting itself as being foreign and directly attacking itself), but rather the immune response simply being so intense that it ends up causing fatal side effects. An example is the Sin Nombre virus, which infects the lungs. When white blood cells release chemicals to kill the virus, they destroy the lining of the aveoli, causing the lungs to fill with fluid. As you might expect, the virus usually harmlessly infects animals (deer mice) and is only dangerous when it infects a species (like humans) that it hasn't adapted to.
Ebola is another example of an animal-bourne virus (it's thought to harmlessly be carried by fruit bats) that is often fatal in humans due to an overagressive immune response.
While they don't randomly change the genome everywhere, cancer cells do represent a mutation of the existing genes. And in particular, the transmissible cancer known as Devil facial tumour disease has very high death rate and is highly transmissible. From the article:
Affected high-density populations suffered up to 100% mortality in 12–18 months. Between 1996 and 2015, DFTD wiped out 95% of affected populations.
Finally, the tumour cells have genetics of their own, not unlike the descolada being a species unto itself:
Researchers sampled 25 tumours and found that the tumours were genetically identical.
In 2015, a second genetically distinct strain of DFTD was identified, which was tetraploid, not diploid like the main form of the cancer.