The following uses zref's savepos module to store the x-coordinate at the call to \fillparbox, as well as the x-coordinate after issuing an \hfill. The difference between these two x-coordinates then provides the width of a \parbox that you can place there:

\documentclass{article}
\usepackage[margin=1in]{geometry}
\usepackage[nopar]{lipsum}
\usepackage{zref-savepos}
\newcounter{fillparbox}
\newcommand{\fillparbox}[2][c]{%
\stepcounter{fillparbox}% New \fillparbox
\mbox{}\zsaveposx{\thefillparbox-L}\hfill\zsaveposx{\thefillparbox-R}% Mark Left and Right end-points remaining on line.
\makebox[0pt][r]{\parbox[#1]{\dimexpr\zposx{\thefillparbox-R}sp-\zposx{\thefillparbox-L}sp}{\strut #2\strut}}%
}
\begin{document}
\lipsum[1]
\fillparbox{\itshape\bfseries one two three four five six seven eight nine ten
eleven twelve thirteen}
\lipsum[2]
\fillparbox{\itshape\bfseries one two three four five six seven eight nine ten
eleven twelve thirteen}
\lipsum[3]
\fillparbox[t]{\itshape\bfseries one two three four five six seven eight nine ten
eleven twelve thirteen}
\end{document}
You can still issue the various alignment options association with \parbox, the default being [c]entred (vertically). \struts are inserted to ensure a consistent baseline (see How to keep a constant \baselineskip when using minipages (or \parboxes)?).
align): Compute remaining horizontal space in align environment. – Peter Grill Aug 17 '17 at 09:28