What term describes a responsibility; someone or something entrusted to the care of another?

The term that describes a responsibility, where someone or something is entrusted to the care of another, is "charge." This concept encompasses the idea of being given the responsibility for something or someone, indicating that there is an expectation to take care of it properly. In various contexts, when someone says they are in "charge" of a task or a person, it signifies that they bear the responsibility to manage or oversee it effectively.

While "obligation," "trust," and "assignment" all relate to responsibilities in a broad sense, they do not embody the same specific meaning as "charge." An obligation refers to a duty or commitment that someone must fulfill, while trust speaks to the confidence placed in someone to act responsibly. An assignment usually suggests a specific task given to someone, but it does not necessarily imply the ongoing responsibility associated with care and oversight that "charge" conveys. Therefore, "charge" is the most fitting term for the scenario presented in the question.