The adjective precarious describes something that is not securely held or not safely fixed, and so is liable to collapse, fail or change at any moment. A precarious ledge may give way, and a precarious livelihood may vanish without warning. Its central idea is the absence of any guarantee or certainty.

The word that shares that core idea is the one that denies assurance: if a thing is not assured, its continuance is uncertain and insecure, which is exactly the sense of the given word.

Accurate means free from error and belongs to the field of measurement, not of safety. Unquestionable means beyond doubt and is close to the opposite, because it asserts certainty where the given word denies it. Vilifying means speaking abusively about somebody and concerns reputation rather than stability, so it bears no relation to the given word.

Unassured option is correct.