How to get one italic Greek letter in math mode when using the upright option with Fourier?

Use \otherrho to typeset the non-default shape of the Greek character \rho. Since the option upright makes upright the default shape, the non-default shape picked up by \otherrho is sloped. Likewise for \otheralpha, \otherbeta, \othergamma, etc.

\documentclass{article}
\usepackage[upright]{fourier}

\begin{document}
    As $\rho\to1{,}000$, we all die.

\em As $\otherrho\to\mathit{1{,}000}$, we all die.
\end{document}

\documentclass{article}
\usepackage{amsmath}
\usepackage[upright]{fourier}

\DeclareFontFamily{U}{pseudofourier}{}
\DeclareFontShape{U}{pseudofourier}{m}{n}{
  <-> futmi
}{}
\DeclareFontShape{U}{pseudofourier}{m}{it}{
  <-> futmii
}{}
\DeclareFontShape{U}{pseudofourier}{b}{n}{
  <-> futmib
}{}
\DeclareFontShape{U}{pseudofourier}{b}{it}{
  <-> futmiib
}{}

\DeclareRobustCommand{\trho}{%
  \text{%
    \fontencoding{U}\fontfamily{pseudofourier}\selectfont
    \symbol{"1A}%
  }%
}

\begin{document}

As $\trho\rightarrow1,000$, we all die.

\textit{As $\mathit{\trho\rightarrow1,000}$, we all die.}

\end{document}

But this is wrong: symbols should not change their shape according to the context.

Use \otherrho to have a slanted Greek letter in an upright setting, and vice-versa. Also I added a pair of braces around the decimal comma to have a correct spacing.

\documentclass{article}
\usepackage[upright]{fourier}

\begin{document}
    As $\rho\rightarrow1{,}000$, we all die.

    \textit{As $\mathit{\otherrho\rightarrow1{,}000}$, we all die.}

\end{document}