In what ways can an analog multiplexer i.c fail? I want to use this in our system ,so i need the complete details of it,so that even if the mux fails,the output should connect to one of the input signals. Is this possible?
It's likely not possible. The most common failure modes for ICs in my experience are for a pin to fail open-circuit, or short-circuited to either power or ground. For an IC to fail with one I/O pin connected to another one is very unlikely.
To get the behavior you want, you'd have to design an ancillary circuit that detects a failure condition (it would have to detect all possible failure conditions) and activates a second multiplexer to select input from the fail-over input instead of from the first mux. And then you'd have to worry about failure modes of that mux...and so on.