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Recommendation: change hyphen "-" into minus sign "−" or en dash "–" when start=-n is used
Minor typographical suggestion. Currently, the MWE
\documentclass[12pt]{article}
\usepackage{enumitem}
\begin{document}
\begin{enumerate}[start=-2] %here n := 2
\item This
\item is
\item just
\item a
\item demo.
\end{enumerate}
\end{document}
gives the output

The hyphen "-" is used for displaying "minus 2", "minus 1" and so on. I recommend changing the default behaviour to the minus sign (−). The en dash (–) is also better than the hyphen if adding the minus sign is unfeasible (en dash = -- in TeX, of course).
This is really a low priority recommendation as a) one rarely needs negative item labels, b) there are easy manual work-arounds. But still a small improvement, in my humble opinion.
Just define a label in math mode: label=$\arabic*$. Or is there any limitation with this solution?