The asymptotic implausibility problem is introduced from the perspective of an adversary that seeks to drive the belief of a recursive Bayesian estimator away from a particular set of parameter values. It is assumed that the adversary controls all sensors informing the estimator, and can transmit false measurements stochastically according to a fixed distribution of its choice. First, we outline a method for verifying whether a given distribution solves the problem. We then consider the class of spoofing attacks, and show that the asymptotic implausibility problem has a solution if and only if it can be solved by a spoofing attack. Attention is restricted to finite parameter and observation spaces.