May be the wrong site, but researching for a writing project... What effect would there be on a group of humans living in a lightless and cramped environment (assume underground) for nearly 800 years, assuming that some form of nourishment is available?
It is unlikely. You have multiple problems to solve quite apart from the inbreeding.
Total lack of light would probably kill them all pretty quickly as they go insane. Insanity would be a major problem pretty quickly, and how would you deal with people who start lashing out in the dark? Discipline would break down into chaos.
Airflow, we can't breathe the same air for 800 years in cramped conditions, there needs to be a source of fresh air.
Food, we cannot live on a single food source, we need a plethora of elements in our diets to remain healthy.
Vitamin D we mostly get from sunlight, without it we need an alternative source.
Many more factors I would think, but the humans themselves would be the worst problem. You can't keep any sort of discipline in this situation and people will go crazy.
Depending on what nourishment exactly is available your humans may suffer from Vitamin D deficiency.
You can get some from food, but mostly quite specific animal products (oily fish, red meat, liver and egg yolks, all of which might be hard to come across in a cave) and the vast majority is created by sunlight on your skin.
The main side effect of a Vitamin D deficiency is soft bones, rickets or osteomalacia. This has a whole host of side effects, the main one being bones break very easily (and in a lightless cramped cave that's probably not a good thing) but also some physical deformities like bowed legs and curvature of the spine, thicker wrists, ankles and knees, and 'pigeon chest’, where the breastbone sticks out.
Combined with inbreeding you might find your population quickly becomes a race of hunchbacks.
You do not say how large your group is. The main problem with an isolated group over 800 years is inbreeding.
The isolation of a small population for a period of time can lead to inbreeding within that population, resulting in increased genetic relatedness between breeding individuals.
Many individuals in the first generation of inbreeding will never live to reproduce. Over time, with isolation, such as a population bottleneck caused by purposeful (assortative) breeding or natural environmental factors, the deleterious inherited traits are culled.
Island species are often very inbred, as their isolation from the larger group on a mainland allows natural selection to work on their population. This type of isolation may result in the formation of race or even speciation, as the inbreeding first removes many deleterious genes, and permits the expression of genes that allow a population to adapt to an ecosystem. As the adaptation becomes more pronounced, the new species or race radiates from its entrance into the new space, or dies out if it cannot adapt and, most importantly, reproduce.
The reduced genetic diversity, for example due to a bottleneck will unavoidably increase inbreeding for the entire population. This may mean that a species may not be able to adapt to changes in environmental conditions. Each individual will have similar immune systems, as immune systems are genetically based. When a species becomes endangered, the population may fall below a minimum whereby the forced interbreeding between the remaining animals will result in extinction.
So too your group. The population will decline after a couple of generations because of inbreeding depression. They might die out. If they don't die out but instead weed out deleterious alleles, there will likely be a pronounced founder effect from the survivors, and these people after 300 years might be fairly different from the starting population.
Some recessive genes which persist into this population might not be so disadvantageous to them; blindness, obviously, but also mutations which produce slowness, lower metabolic rate etc. There may be mutations which are irrelevant to the lightless circumstances but which arise because of chance and the founder effect - for example, they all have unusually shaped ears. If their environment exerts any sort of selective pressure on them (you decide) such that certain characteristics improve the likelihood of leaving children, you could have selection for those characteristics.
800 years is not very long for humans, evolutionarily. But evolution can happen fast in isolated groups.