By using Figure~\subref*{sfig:sfig1} the only possible breaking points are to hyphenate "Figure" or to break after the whole expression. With the default settings LaTeX does not do the linebreak by hyphenating "Figure" because then the line would be underful. If you make the spaces a bit stretchier by using \emergencystretch=.5em, the new linebreak will hyphenate "Figure".
Of course this might result in spaces which are larger than desired from a typographical point of few. In this case rephrasing the sentence can avoid the problem.
\documentclass{report}
\usepackage[caption=false,subrefformat=parens,labelformat=parens]{subfig}
\emergencystretch=.5em
\begin{document}
\setcounter{chapter}{10}
\chapter{Chapter title}
\begin{figure}[h]
\centering
\subfloat[Subcaption.]{\rule{100pt}{50pt}\label{sfig:sfig1}}
\caption{Caption.}
\label{fig:Fig1}
\end{figure}
sample text sample text sample text sample text sample text saa Figure~\subref*{sfig:sfig1} sample text sample text sample text sample text
\end{document}

A small suggestion: With the cleveref package it is not necessary to manually write Figure~:
\documentclass{report}
\usepackage[caption=false,subrefformat=simple,labelformat=simple]{subfig}
\usepackage[capitalise,noabbrev]{cleveref}
\renewcommand{\thesubfigure}{(\alph{subfigure})}
\emergencystretch=.5em
\begin{document}
\setcounter{chapter}{10}
\chapter{Chapter title}
\begin{figure}[h]
\centering
\subfloat[Subcaption.]{\rule{100pt}{50pt}\label{sfig:sfig1}}
\caption{Caption.}
\label{fig:Fig1}
\end{figure}
sample text sample text sample text sample text sample text saa Figure~\subref*{sfig:sfig1} sample text sample text sample text sample text
sample text sample text sample text sample text sample text saa \cref{sfig:sfig1} sample text sample text sample text sample text
\end{document}
cleverefpackage you could automatically insertFigure~– samcarter_is_at_topanswers.xyz May 08 '18 at 16:39\refis not fair . If one changessaatosame, to make both lines the same length, "Figure" is also hyphenated for\subref. The other way round, I can provoke an overfull box with\refif I change the chapter counter to 100. – samcarter_is_at_topanswers.xyz May 08 '18 at 16:42\emergencystretch=.5em– samcarter_is_at_topanswers.xyz May 08 '18 at 16:52