return {} when the function is given {}

Actually, I want the output to be {} if there is anything wrong with the argument.

For this I recommend one or more definitions with patterns that only match a valid argument, and a fall-through definition for anything else. For example if the argument should be a nonempty list of integers:

(* primary definition *)
func[arg : {__Integer}] := Mean[arg]

(* fall-through definition *)
_func := {}

test:

func[{1, 2, 3}]
func[{1.23}]
func[{}]
func[1, 2, 3]

2

{}

{}

{}

Additional reading:

• How to check the style and number of arguments like the built-in functions?
• Quick way to use conditioned patterns when defining multi-argument function?

One way is to make some definitions

foo[arr_] := {}
foo[{}] := {} 
foo[arr_List] := "ok"

Mathematica will automatically pick the correct definition to use.