Software Failure?
I doubt there is any such thing. Software just is whatever has been coded. Unless the memory media on which it is stored fails somehow, the software remains intact, just as coded and compiled.
Software error? Yes, and as so many have explained, testing to find every software error (AKA bug) is fairly impractical in the large bodies of complex code used in avionics, engines and such. So rather than completely exhaustive testing, though some testing indeed is done, there is required to be a disciplined software development process, the rigor of which is driven by the safety effects that a function affected by software error might be considered to have.
Highly critical functions with potentially catastrophic effects from software errors must have a "design assurance level" of A, which of course is the highest and most expensive development process.