The comment was a little sloppy. Let $N$ be a norm in $\mathbb{R}^2$. Then the unit ball is the set of all points in $\mathbb{R}^2$ whose norm is one. So for example if we consider the Euclidean norm, then
$$N(-1,0)=N(0,-1)=N(0,1)=N(1,0)=N\left(-\frac{1}{2},-\frac{\sqrt{3}}{2}\right)=1$$
so all five of these points are on the unit ball. Since the norm is defined for all of the points in the plane, the input to the norm function can be anything, positive, zero, negative. The output must always be nonnegative.
To disambiguate my comment, when I wrote the comment I was thinking only of $\mathbb{R}$ with $N(x)=|x|$ to show that the input to a norm function can be negative. For a generic dimension, we can always use $N(\vec{x})$ where $\vec{x}$ is a vector of whatever type we need it to be.
