Question: It is true that a lot of members of our, and most other species, suffer from cancer, but it is still not ubiquitous nor does it exist throughout the individual's life.

If a species existed, in which all, or almost all of its members suffered from the same pathology, and that pathology showed up and existed throughout the organism's life, and this pathology has always existed within the species, would that violate natural selection enough to consider the current body of theory of evolution falsified?

To be clear, it is recognized that natural selection is not the only process which occurs during evolution, but it is pretty safe to say that enough of our body of theory on evolution rests with the validity of natural selection that if natural selection were falsified, so would the body as a whole, and we would need to rework our theories.

Consider what is said in *[Evolutionary dynamics in structured populations](https://www.ncbi.nlm.nih.gov/pmc/articles/PMC2842709/)*. 

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> An evolving population consists of reproducing individuals, which are information carriers. When they reproduce, they pass on information. New mutants arise if this process involves mistakes. Natural selection emerges if mutants reproduce at different rates and compete for limiting resources.
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In other words, evolutionary dynamics implies natural selection. A violation of natural selection therefore would make the current theory on evolutionary dynamics less likely. Now, it could be that other processes are so powerful that they completely override natural selection, but to find a species in which natural selection has totally failed to weed out a near universal illness should present a problem for current evolutionary theory.

Answer: 
Very short answer
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Evolution ≠ Natural Selection

Slightly longer answer
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**Evolution ≠ Natural Selection**

You seem to equate evolution with natural selection which is the main issue. Various evolutionary processes may yield a population where all individuals suffer from a specific disease. It may not be an equilibrium state though but a state that may well last long enough to be frequently observed.

For example a [bottleneck](https://en.wikipedia.org/wiki/Population_bottleneck) can cause a disease to reach an extremely high frequency if there was some deleterious recessive alleles in the parent population. A bottleneck is not a process that is encompass within the term Natural Selection but it is still an evolutionary process.

We actually have examples (incl. examples in humans) of populations where the prevalence of particular genetic disease is very high.

**The existence of other evolutionary processes than natural selection does not violate the theory of natural selection**

The existence of other evolutionary processes than natural selection does not violate natural selection theory. The theory of natural selection does not state that nothing but natural selection can affect a population's evolution.

If one were to think that the existence of genetic drift (another evolutionary process) would violate natural selection, then this person would also think that the existence of wind that would affect an apple course falling through the air would violate the theory of gravitation.

**What is evolution?**

Your question comes from a misrepresentation of what evolution is about. You might want to have a look at a short and intro course to evolutionary biology such as [Understanding Evolution by UC Berkeley](http://evolution.berkeley.edu/evolibrary/article/evo_01) for example.
**Evolution doesn't ensure a good quality of life, nor does it ensure a longer lifetime of a species's organism.**. It only ***aims for the continued sustenance of the species*** in a changing environment. 

What does being ill really mean? 

* Does it mean that the lifespan becomes smaller? No, an insect might have a smaller lifespan while being a very rapidly evolving life form.
* Does it mean that the species would be pain-free while living? No, even humans are designed to endure chronic pain.

All the things that contribute to not being "ill", are really just things which contribute to being able to have a faster and continuous sustenance. Long life means more chances of offsprings, being pain-free gives more time and ability to mate. 

Hope this answers your question! First post. This thread made me join this exchange!