Using the float package, you can stuff figures inside minipages. However, the whole assembly will then no longer float.
\documentclass{article}
\usepackage{float}
\usepackage{mwe, boxedminipage,calc}
\usepackage[margin=0.5in,papersize={4in,4.5in}]{geometry}
\pagestyle{empty}
\begin{document}
\noindent Text before \bigskip
\noindent
\begin{boxedminipage}{\linewidth}
\begin{boxedminipage}{\linewidth}
\centering
\begin{figure}[H] % the H must be here, or you will get 'not in outer par mode' error
\includegraphics[width=0.8\linewidth]{/data/graphics/fun/asterix/switzerland-red-cross}
\caption{This is the first figure}
\end{figure}
\end{boxedminipage}
\medskip
\begin{boxedminipage}{\linewidth}
\centering
\begin{figure}[H]
\includegraphics[width=0.8\linewidth]{/data/graphics/fun/asterix/switzerland-red-cross}
\caption{This is the second figure}
\end{figure}
\end{boxedminipage}
\end{boxedminipage}
\bigskip
\noindent Text after
\end{document}
Result:

This was adapted from How to use figure inside a minipage?
subcaption, butsubfig. Also, where does it say thatlifecondoesn't work withsubcaption? At first glance it doesn't look like there is anything inlifecon.stythat would conflict withsubcaption, and compiling a document with both packages works fine, no errors or warnings. – Torbjørn T. Oct 28 '16 at 15:53