Is respiratory failure curable, or is the person doomed?

Varies. Some will recover quickly. Some may need months of weaning therapy to get off ventilator. Some will never breathe on own. Depends entirely on cause, as it is a symptom of many problems. Resp failure does not always mean lung problem-just inability to exchange oxygen and carbon dioxide enough to live or protect airway, so can be due to sepsis, heart failure, muscle dz, brain damage, etc.
Depends on etiology. Prognosis for respiratory failure depends on severity, etiology as well as other system disease. For example, a young otherwise healthy patient in respiratory failure due to pneumonia has a better prognosis than a very old person in respiratory failure due to lung cancer who is also in kidney failure. So, it depends on the situation whether or not the patient is "curable.".
Respiratory Failure. Can occur for with a number of conditions that are reversible, so depending on the source for the respiratory failure, it may not be fatal. Those with end stage emphysema or copd, once they go into respiratory failure, are at a much higher risk of dying from respiratory failure.