\looparrowright but without the arrow tip

You can clip the symbol:

\documentclass{article}
\usepackage{amssymb}
\usepackage{trimclip}

\makeatletter
\DeclareRobustCommand{\leftloop}{%
  \mathrel{\mathpalette\left@loop\relax}%
}
\newcommand{\left@loop}[2]{%
  \vphantom{\looparrowright}
  \smash{\clipbox{0 {-.1\height} {.35\width} {-.1\height}}{$\m@th#1{\looparrowright}$}}%
}
\makeatother

\begin{document}

$a\leftloop b_{c\leftloop d}$

\end{document}

Code borrowed from https://tex.stackexchange.com/a/395049/4427

This means “cut nothing on the left, add a negative clip on the bottom, clip 35% of the width from the right, add a negative clip on the top”. Why negative clipping? Because the glyph slightly overshoots its bounding box. So I also smash the clipped symbol and set the height with the help of \vphantom.

Can we keep the round cap? Yes, by adding a clipped minus sign.

\documentclass{article}
\usepackage{amssymb}
\usepackage{trimclip}

\makeatletter
\DeclareRobustCommand{\leftloop}{%
  \mathrel{\mathpalette\left@loop\relax}%
}
\newcommand{\left@loop}[2]{%
  \smash{\clipbox{0 {-.1\height} {.4\width} {-.1\height}}{$\m@th#1{\looparrowright}$}}%
  \clipbox{{0.8\width} 0 0 0}{$\m@th#1-$}%
  \mkern-1mu
}
\makeatother

\begin{document}

\fboxrule=0.1pt\fboxsep=0pt\fbox{$\leftloop$}% just to see the bounding box

$a\leftloop b_{c\leftloop d}$

\end{document}

No need to add a phantom, because the minus sign has the right height and depth.

• Please go with eger's answer - I just was inspired by his comment and tried it myself.
• I use the adjustbox package.
• @pros Please indicate if my solution has some problems (apart from being too simplistic).
• This is a trial-and-error approach :).

---

\documentclass{article}
\usepackage{adjustbox}
\usepackage{amssymb}

\begin{document}

\begin{itemize}
    \item \adjustbox{trim = 0 0 1 0, clip}{\fbox{Test $a$}} \fbox{Test $a$}
    \item \adjustbox{trim = 0 0 7 0, clip}{\fbox{$\looparrowright$}} \fbox{$\looparrowright$}
    \item \adjustbox{trim = 0 0 4 0, clip}{$\looparrowright$}
\end{itemize}

\newcommand{\myLoop}{\adjustbox{trim = 0 0 4 0, clip}{\ensuremath{\looparrowright}}}

\myLoop

\end{document}