It is rather easy to do with the calc library.
\documentclass[tikz,border=3.14mm]{standalone}
\begin{document}
\usetikzlibrary{shapes.geometric,calc}
\begin{tikzpicture}
\tikzset{interface/.style={draw,regular polygon,regular polygon sides=8}}
\node[draw] (ec) {Erasure correction};
\node[below of=ec] (eci) {Erasure Correction Interface};
\path let \p1=($(eci.east)-(eci.west)$) in
node[interface,minimum width=\x1+5pt] at (eci){};
\end{tikzpicture}
\end{document}

You might use some standard values for the gap as well. In the end it depends on what you precisely want to achieve. There are a number of standard distances at play, once I know better what the goal is I may be able to adjust the following to your needs.
\documentclass[tikz,border=3.14mm]{standalone}
\begin{document}
\usetikzlibrary{shapes.geometric,calc}
\begin{tikzpicture}
\tikzset{interface/.style={draw,regular polygon,regular polygon sides=8}}
\node[draw] (ec) {Erasure correction};
\node[below of=ec] (eci) {Erasure Correction Interface};
\path let \p1=($(eci.east)-(eci.west)$) in
node[interface,minimum width=\x1+2*\pgfkeysvalueof{/pgf/inner
xsep}+2*\pgflinewidth] at (eci){};
\end{tikzpicture}
\end{document}

UPDATE: As for the clarified question: it is rather easy to cook up something along those lines using path picture
. I did not know, however, what determines the sizes of the cut corners. So I choose inner sep
since that way the boundary won't run into the text.
\documentclass[tikz,border=3.14mm]{standalone}
\begin{document}
\usetikzlibrary{shapes.geometric,calc,positioning}
\begin{tikzpicture}[]
\tikzset{interface/.style={draw,regular polygon,regular polygon sides=8},
my octagon/.style={path picture={
\draw
([yshift=\pgfkeysvalueof{/pgf/inner ysep},xshift=\pgflinewidth/2] path picture bounding box.south west)
--([yshift=-\pgfkeysvalueof{/pgf/inner xsep},xshift=\pgflinewidth/2] path picture bounding box.north west)
--([xshift=\pgfkeysvalueof{/pgf/inner xsep},yshift=-\pgflinewidth/2] path picture bounding box.north west)
--([xshift=-\pgfkeysvalueof{/pgf/inner xsep},yshift=-\pgflinewidth/2] path picture bounding box.north east)
--([yshift=-\pgfkeysvalueof{/pgf/inner ysep},xshift=-\pgflinewidth/2] path picture bounding box.north east)
--([yshift=\pgfkeysvalueof{/pgf/inner ysep},xshift=-\pgflinewidth/2] path picture bounding box.south east)
--([xshift=-\pgfkeysvalueof{/pgf/inner xsep},yshift=\pgflinewidth/2] path picture bounding box.south east)
--([xshift=\pgfkeysvalueof{/pgf/inner xsep},yshift=\pgflinewidth/2] path picture bounding box.south west)
--cycle;
}}}
\node[draw] (ec) {Erasure correction};
\node[below=3mm of ec,my octagon] (eci) {Erasure Correction Interface};
\node[below=3mm of eci,my octagon,inner sep=5mm] (ecf) {Erasure Correction Failure};
\end{tikzpicture}
\end{document}

It is of course possible to tie the dimensions of the cut corners to other length scales, which one may introduce just for that purpose. However, before showing too many options I'd like to know where the journey is supposed to go, i.e. I need clearer instructions.
inner sep
).inner sep=-5mm
to reduce the margin between contents and border\node[draw, rectangle, rounded corners, below of=ec] (eci) {Erasure Correction Interface};