You can use the same basic idea as in Functionality of apacites \nocitemeta with biblatex-apa: adding asterisks to author lastnames (meta-analysis).
We just need to print the symbol in the field format labelnumberwidth instead of in the begentry bibmacro to ensure the symbol appears before the label number.
\documentclass[american]{article}
\usepackage[T1]{fontenc}
\usepackage[utf8]{inputenc}
\usepackage{lmodern}
\usepackage{babel}
\usepackage{csquotes}
\usepackage[style=ieee,
sorting=ydnt,
maxbibnames=99,
url=false,doi=false,
dashed=false,
]{biblatex}
\newtoggle{bib@corresponding}
\DeclareEntryOption{corresponding}[true]{\settoggle{bib@corresponding}{#1}}
\DeclareFieldFormat{labelnumberwidth}{%
\iftoggle{bib@corresponding}%
{\textdagger}%
{}%
\mkbibbrackets{#1}%
}
\defbibnote{corresponding}{\textdagger\ indicates applicant is (co-) corresponding author.}
\begin{filecontents}{\jobname.bib}
@book{bohec,
author = {Le Bohec, Yann},
title = {Histoire militaire des guerres puniques},
date = {1996},
location = {Monaco},
publisher = {Rocher},
isbn = {2-268-02147-5},
options = {corresponding},
}
@book{uthor,
author = {Uthor, Arnold},
title = {A Book},
date = {2013},
location = {Place},
publisher = {P. Ublisher's & Co.},
}
\end{filecontents}
\addbibresource{\jobname.bib}
\begin{document}
\autocite{bohec,uthor}
\printbibliography[postnote=corresponding]
\end{document}

Different markers can be added analogously.
\documentclass[american]{article}
\usepackage[T1]{fontenc}
\usepackage[utf8]{inputenc}
\usepackage{lmodern}
\usepackage{babel}
\usepackage{csquotes}
\usepackage[style=ieee,
sorting=ydnt,
maxbibnames=99,
url=false,doi=false,
dashed=false,
]{biblatex}
\newtoggle{bibentry@corresponding}
\DeclareEntryOption{corresponding}[true]{\settoggle{bibentry@corresponding}{#1}}
\newtoggle{bibentry@cofirst}
\DeclareEntryOption{cofirst}[true]{\settoggle{bibentry@cofirst}{#1}}
\DeclareFieldFormat{labelnumberwidth}{%
\iftoggle{bibentry@corresponding}%
{\textdagger}%
{}%
\iftoggle{bibentry@cofirst}%
{\textdaggerdbl}%
{}%
\mkbibbrackets{#1}%
}
\defbibnote{corresponding}{\textdagger\ indicates applicant is (co-) corresponding author.}
\begin{filecontents}{\jobname.bib}
@book{bohec,
author = {Le Bohec, Yann},
title = {Histoire militaire des guerres puniques},
date = {1996},
location = {Monaco},
publisher = {Rocher},
isbn = {2-268-02147-5},
options = {corresponding},
}
@book{uthor,
author = {Uthor, Arnold},
title = {A Book},
date = {2013},
location = {Place},
publisher = {P. Ublisher's & Co.},
options = {cofirst},
}
\end{filecontents}
\addbibresource{\jobname.bib}
\begin{document}
\autocite{bohec,uthor}
\printbibliography[postnote=corresponding]
\end{document}