Recently, a fail-safe principle in wide sense was proposed by one of the authors, in order to accomplish the flexible security against accidents or failures. This new principle is established by the following idea: i.e., if the tolerable range of the deviated output response as a behavior of system is definitely estimated, in advance, and if the response can be found in this range, we can always use this response as available. Even if the deviation range of the output response extends far from the tolerable one, it is sufficient that the system itself has a methodology to find the available response in the tolerable range, and the system behaves by this response. This new concept of an extended type of the fail-safe principle is a significant application of the mathematical theory of nondeterministic fluctuations of systems which was presented by the authors. In this paper, the foundation is given to this principle by developing its mathematical theory, in detail.