Since agents are a structure, it is possible to put an agent in an environment in which it is not possible for that agent to perform optimization. This is an edge case in an otherwise robust generalization that agents are a type of optimizer.
It is common in the related literature to focus entirely on behavioral definitions of agents, to the point where an “unsuccessful agent” would feel totally contradictory to some researchers. We believe that if you take a real implementation of, say, a utility maximization algorithm, and place it in an environment like those below, then it should still be classified as an agent and detected by formal definitions.
There are many types of environment that could prevent an agent from achieving its values. The agent could;