If someone sleeps for three hours a night for three months, what will happen to !

If someone sleeps for three hours a night for three months, what will happen to their body and mind?

Will it "shut down"? If so, how exactly?

Will they be okay?

Well, you'll suffer from long term sleep deprivation. Your mind and body can't recharge properly. Your nervous systems starts to behave like you're drunk, i.e. give you lower response times, tunnel vision, risky behaviour and such.
You can get very edgy and aggressive, and it can lead to depression (also, a lot of people who suffer from clinical depression sleep little).
Sleep disturbance for more than two weeks is a risk factor for developing depression.

From "Sleepfoundation.org":
Sleep deprivation has been linked to health problems such as obesity and high blood pressure, negative mood and behavior, decreased productivity, and safety issues in the home, on the job, and on the road.
For example, insufficient sleep affects growth hormone secretion that is linked to obesity; as the amount of hormone secretion decreases, the chance for weight gain increases. Blood pressure usually falls during the sleep cycle, however, interrupted sleep can adversely affect this normal decline, leading to hypertension and cardiovascular problems. Research has also shown that insufficient sleep impairs the body's ability to use insulin, which can lead to the onset of diabetes.