Whatever encoding you invent, I can give you an infinite input stream of bits that makes your decoder hang and never give a definite answer like "yes, this is an integer with such-and-such value" or "no, this isn't a valid encoding of any integer".

What if my encoding is: return TRUE(=is an integer) for all inputs?

That's not such a dumb thing to do. In fact, any encoding that didn't assign some integer outcome to any sequence of bits would be trivially suboptimal.