Which term indicates a state of being infallible or without error?

The term that indicates a state of being infallible or without error is "foolproof." This word is commonly used to describe systems, processes, or plans that are designed to be reliable and without fail, meaning that, under normal circumstances, they will work perfectly and not lead to mistakes or problems. The essence of "foolproof" lies in its implication that even a person who may not be skilled or knowledgeable will be able to succeed without making any errors.

Other options don't share this meaning. "Fragile" refers to something that is delicate and easily broken, indicating a lack of robustness rather than infallibility. "Forfeit" pertains to losing something as a penalty, which does not relate to being error-free. "Forgive" deals with the process of excusing a mistake or offense, which implies that errors have occurred, contrasting sharply with the concept of being without error.

Thus, "foolproof" is the most appropriate choice for describing a state of being infallible or without error.