For that matter is it even signed? When I visited Liechtenstein I don't remember seeing any signage for it and I was looking.
Technically there are a couple of signs with 16 cartouches in Liechtenstein, but they do both squarely point towards Switzerland shortly before the border. Regardless, it's enough for me to be willing to go "eh, close enough" at LIE H16 being signed.
This is like WY 70 where it dips into Colorado (https://travelmapping.net/hb/showroute.php?u=null&r=co.wy070)
I don't think it's analagous because WY 70 exits
and then reenters Wyoming. While a few examples are in the HB based on field signage, I do not believe there is officially, on paper, any example in the US of a state route that exits its parent state and does not subsequently reenter it. All cases in the HB are inventoried as something else on the far side of the state line.
Nonetheless, the fact that the Swiss government's website shows H16 going to Austria would appear to confirm that it is in fact their road. Strange. But so it goes.