Can a \hbox be made to attain all of its surrounding space?

This doesn't answer your question, but perhaps you want something like this?

\documentclass{article}
\makeatletter
\newcommand\labeleddownbracefill[1]{%
        $\m@th
        \setbox\z@\hbox{$\braceld$}%
        \braceld
        \leaders\vrule\@height\ht\z@\@depth\z@\hfill
        \braceru
        \raise1ex\hbox to\z@{\hss$\scriptstyle#1$\hss}%
        \bracelu
        \leaders\vrule\@height\ht\z@\@depth\z@\hfill
        \bracerd
        $%
}
\makeatother
\begin{document}
\begin{tabular}{cc}
foo&\labeleddownbracefill{\lambda}\\
bar&Here is some text to be braced\\
\end{tabular}
\end{document}