 Quantile endpoint at probability one

The quantile function is finite at every probability strictly between zero and one, but need not be finite at one. For any unbounded-above normal distribution, $F(x)<1$ for every real $x$, so its generalized inverse at one is $+\infty$. Inverse transform sampling still produces a real random variable almost surely because a continuous uniform distribution puts zero mass at that endpoint. A real-valued implementation may discard endpoint draws or assign an arbitrary finite value there without changing the sampled law.