There will always be one person who is ultimately responsible. In the corporate world this is the CEO, in other business structures it could the majority partner, the owner, etc.
Nonprofits are no different in this regard. There is going to be one person who bares the ultimate responsibility for the success or failure of the nonprofit. Regardless of the size of the organization. In general as the annual contributions increase there is more structure put in place. This structure often includes a board to oversee things and provide direction, a director to execute on that direction, and different departments and roles underneath them. So there may not be a CEO (since that is a corporate term that may not apply to the structure of the nonprofit) there will be a person in a comparable role.
