You're allowed to invent an arbitrary scheme for encoding integers as strings of bits. 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".

I find it annoying how my brain keeps saying "hah, I bet I could" even though I explained to it that it's mathematically provable that such an input always exists. It still keeps coming up with "how about this clever encoding?, blablabla" ... I guess that's how you get cranks.