I'm used to this definition:
In engineering, a
fail-safe is a design feature or practice that in the event of a specific type of
failure, inherently responds in a way that will cause no or minimal harm to other equipment, the environment or to people. Unlike
inherent safety to a particular hazard, a system being "fail-safe" does not mean that failure is impossible or improbable, but rather that the system's design prevents or mitigates unsafe consequences of the system's failure. That is, if and when a "fail-safe" system fails, it remains at least as safe as it was before the failure.
[1][2] Since many types of failure are possible,
failure mode and effects analysis is used to examine failure situations and recommend safety design and procedures.