What term describes a trade or business where all the work is done without compensation for the organization?

The term that best describes a trade or business where all the work is performed without receiving any compensation for the organization is "volunteer service." In this context, volunteer service refers specifically to activities carried out by individuals who contribute their time and effort without financial remuneration. These services may support a charitable or non-profit organization, enhancing its offerings or operations without the expectation of payment.

While the notion of unrelated business income (UBI) often arises in discussions of non-profit organizations, particularly in relation to UBI conditions or excluded activities, those terms relate more to the classification and treatment of income rather than to the nature of voluntary involvement. Therefore, while they might be relevant in certain financial or tax contexts, they do not encapsulate the essence of work performed without compensation as effectively as the term "volunteer service" does.