It happens in lot of organization. Its a management habit in some organization who think of cutting corners , that they are saving money.

These management people tend to overlap responsibilities. What I mean is if a person is recruited to be an administrative assistant for the entire department of say 20 people, with years he become manager's and Team leader's personal assistant, some time top people's driver, etc. This is one example. Other example in short would be Sales staff taking up finance tasks or Production's responsibilities, and so on. 

This is not exactly "spreading too thin" while sure that is the side effect. But the main effect is the same person is absent for his original responsibilities and the the culture and the atmosphere is in chaos and wrong message is being sent.

The reason why i am asking this phrase is because it is probably already available on wikipedia or such sites which articulates its pros and cons which i have to present to a external agency which is recruited by our company to revamp the organization. I have tries on wikipedia but has not results.I am not sure it might be a single word