Biggest depth of a character in a string

I don't know about your approach using a loop, but to get the depth, just use \settodepth

See : https://tex.stackexchange.com/a/37294/116936

You can also use the calc package \depthof

\documentclass{article}

\begin{document}
\def\mystring{abcdefgh}
\newlength\myLength

\settodepth{\myLength}{\mystring}

\the\myLength
\end{document}

Cheers,

The answer by marsupilam covers how one would normally achieve the task: typeset the content and get the box depth.

There are two issues with the code you've got. First, the TeX primitive \dimen has to be followed by a register number, not by an =. Using the fact that \dimen0 is a scratch register in LaTeX, you therefore can use \dimen0=<some valid dimension>. The second is that \StrMid doesn't generate a letter per se (it's not 'expandable'), it is instructions to do that in a typesetting context. However, there is an optional argument that will 'return' what you want

\StrMid{\mystring}{\X}{\X}[\tmp] % \tmp now expands to the substring

We can use that with \expandafter to get what \fontchardp requires: the character number you are interested in

\documentclass{article}
\usepackage{xstring}

\begin{document}

\def\mystring{abcdefgh}
\StrLen{\mystring}[\len]
\newcount\X
\X=\len

\loop
  \StrMid{\mystring}{\X}{\X}[\tmp]
  \dimen0=\fontchardp\expandafter\font\expandafter`\tmp
  \edef\x{\tmp\space\the\dimen0 }%
  \show\x
  \advance \X by -1 %
  \unless\ifnum \X<1 %
\repeat

\end{document}

(I've show rather than typeset the result)

Similar to Joseph’s, but using less code

\documentclass{article}
\usepackage{xstring}

\newcount\X
\newdimen\stringdepth

\begin{document}

\def\mystring{abcdefgh}
\StrLen{\mystring}[\len]

\X=0
\stringdepth=0pt

\loop
  \ifnum\len>\X
  \advance\X by 1
  \StrChar{\mystring}{\X}[\tmp]%
  \begingroup\edef\x{\endgroup
    \dimen0=\fontchardp\font`\tmp\relax
  }\x
  \ifdim\dimen0>\stringdepth \stringdepth=\dimen0 \fi
  % just for showing the work
  \typeout{\tmp\space has depth \the\dimen0 }%
\repeat

\typeout{Max depth: \the\stringdepth}

\end{document}

Of course

\settodepth{\stringdepth}{\mystring}

is much more efficient.

A different loop, quite flexible, as shown by the examples: the current item is referred to as #1 in the final argument to \stringloop:

\documentclass{article}
\usepackage{xparse}

\ExplSyntaxOn
\NewDocumentCommand{\stringloop}{smm}
 {
  \IfBooleanTF{#1}
   { % we have a macro as argument
    \tl_map_inline:Nn #2 { #3 }
   }
   { % an explicit token list
    \tl_map_inline:nn { #2 } { #3 }
   }
 }
\ExplSyntaxOff

\newdimen\stringdepth

\begin{document}

\def\mystring{abcdefgh}

\stringloop{abcdefgh}{\typeout{#1 has depth \the\fontchardp\font`#1}}

\stringdepth=0pt
\stringloop*{\mystring}{%
  \ifdim\fontchardp\font`#1>\stringdepth
    \stringdepth=\fontchardp\font`#1\relax
  \fi
}
\typeout{Max depth in \mystring: \the\stringdepth}

\end{document}

Here is the output on the terminal (and log file):

a has depth 0.0pt
b has depth 0.0pt
c has depth 0.0pt
d has depth 0.0pt
e has depth 0.0pt
f has depth 0.0pt
g has depth 1.94444pt
h has depth 0.0pt
Max depth in abcdefgh: 1.94444pt