Consider the moduli of smooth curves $M_{g,n}$ (genus $g$, $n$ marked points) and its Deligne-Mumford compactification $\overline{M}_{g,n}$ of *stable* nodal curves (genus $g$, $n$ marked points). This is usually only defined for $2g-2+n>0$. It seems the point of this condition is that $M_{g,n}$ has no infinite automorphisms. (For example for genus 0, we need to specify three marked points in order to pin down a unique automorphism of the curve.) Stability of a nodal curve can then be defined to mean that the automorphism groups are finite, which can be characterized in terms of the irreducible components of the normalization.

Here's my question, is it possible to give a useful definition of $\overline{M}_{g,n}$ when $2g-2+n \le 0$? I guess defining "stable" in terms of finite automorphisms is a bad idea in this case because then $M_{g,n}$ will not be contained in side $\overline{M}_{g,n}$. So is there another definition that will still give us a proper algebraic stack (possibly in the sense of Artin, i.e., just allow infinite automorphisms)?

Any references are appreciated, the ones I looked at all have this numerical condition on $g,n$. I guess it is because algebraic stacks in the Artin sense are too complicated to work in practice. But I am still curious about it.