A man's gotta live up to his committments according to the priorities established by society if he is to have integrity in the eyes of his peers. Allowing for the severity of the cause, it is expected that your actions would be dicated by the priorities of your committments. Family issues generally take precedence over work issues. Everyone knows and expects this as the standard today. Anyone who doesn't should not expect to employ people with any sense of loyalty, committment or trustworthiness.

Given the grievous nature of the condition, I would expect my employees to see to their personal affairs ahead of their obligations to the work. If they were not so inclined, I would have serious doubts as to their reliability and judgement. In fact, I would fairly insist they leave to deal with the matter because it will likely be a big enough distraction otherwise they would be worthless to me at best, and more likely create a serious hazard.