The package detects this and warns that the final frame segment at the page break is empty. It does however output the segment, otherwise you would not get the
final border of the frame.
here though you only have side borders so (I think, I don't know this code that well) it is safe just to discard the final segment. It seems to work here at least. (See the two places marked CHANGE)

\documentclass[a4paper,11pt,fleqn]{report}
\setlength{\headheight}{15pt}
\setlength{\textheight}{430pt}
\renewcommand{\arraystretch}{1.3}
\usepackage{amsmath}
\usepackage[bold-style=ISO]{unicode-math} % must come after ams and symbols
\usepackage{xcolor}
\usepackage{mdframed}
\makeatletter
\def\mdf@put@frame@ii{%
\setlength{\mdf@freevspace@length}{\vsize}%
\ifbool{mdf@repeatframetitle}%
{%repeating title -- more robust using hooks.
\toggletrue{mdf@notfirstframetitle}%
\splitmaxdepth\z@ \splittopskip\z@%
\setbox\mdf@splitbox@one=\vbox{\break\unvbox\mdf@splitbox@one}%
\mdf@ignorevbadness%
\setbox0=\vsplit\mdf@splitbox@one to \z@\relax%
\setbox\mdf@splitbox@one=\vbox{\unvbox\mdf@splitbox@one}%
\setbox\mdf@splitbox@one\vbox%
{%
\parskip\z@\relax%
\parindent\z@\relax%
\vskip\mdf@frametitleaboveskip@length%
\unvcopy\mdf@frametitlebox\relax%
\mdf@@frametitlerule\relax%
\unvbox\mdf@splitbox@one\relax%
}%
\setbox\mdf@splitbox@one=\vbox{\unvbox\mdf@splitbox@one}%
}{}%
\setlength{\dimen@}{\dimexpr\ht\mdf@splitbox@one+\dp\mdf@splitbox@one\relax}%
\mdf@dolist{\mdf@advancelength@add{\dimen@}}%
{innerbottommargin,innerlinewidth,middlelinewidth,outerlinewidth}%
\ifboolexpr { bool {mdf@everyline} and bool {mdf@topline} }%
{%
\mdf@dolist{\mdf@advancelength@add{\dimen@}}%
{innerlinewidth,middlelinewidth,outerlinewidth}%
}{}%
\notbool{mdf@bottomline}%remove bottom if neccessary
{%
\mdf@dolist{\mdf@advancelength@sub{\dimen@}}%
{innerlinewidth,middlelinewidth,outerlinewidth}%
}{}%
\ifdimgreater{\dimen@}{\mdf@freevspace@length}%
{%have a middle box
\advance\mdf@freevspace@length by -\mdf@splitbottomskip@length\relax%
\ifbool{mdf@everyline}%regard top and bottom if everyline is used
{%
\ifbool{mdf@topline}%
{%
\mdf@dolist{\mdf@advancelength@sub{\mdf@freevspace@length}}%
{innerlinewidth,middlelinewidth,outerlinewidth}%
}{}%
\ifbool{mdf@bottomline}%
{%
\mdf@dolist{\mdf@advancelength@sub{\mdf@freevspace@length}}%
{innerlinewidth,middlelinewidth,outerlinewidth}%
}{}%
}{}%
\setbox\mdf@splitbox@save=\vbox{\unvcopy\mdf@splitbox@one}%
\splitmaxdepth\z@ \splittopskip\mdf@splittopskip@length%
\mdf@ignorevbadness%
\setbox\mdf@splitbox@two\vsplit\mdf@splitbox@one to \mdf@freevspace@length%
\setbox\mdf@splitbox@two\vbox{\unvbox\mdf@splitbox@two}%
\setbox\mdf@splitbox@one\vbox{\unvbox\mdf@splitbox@one}%
\ifdimgreater{\ht\mdf@splitbox@two+\dp\mdf@splitbox@two}%
{\mdf@freevspace@length}%
{%splitted wrong
\mdf@PackageInfo{Box was splittet wrong^^J
starting loop to iterate
the splitting point\MessageBreak}%
\dimen@i=\mdf@freevspace@length%\relax
\@tempcnta=\z@\relax
\loop
\ifdim\dimexpr\ht\mdf@splitbox@two+\dp\mdf@splitbox@two\relax>%
\mdf@freevspace@length\relax
\advance\dimen@i by -\p@\relax%
\advance\@tempcnta by \@ne\relax%
\ifnum\@tempcnta>100
\let\iterate\relax%
\mdf@PackageWarning{correct box splittet fails^^J
It seems you are using a non splittable
contents\MessageBreak}%
\fi
\mdf@ignorevbadness%
\setbox\mdf@splitbox@one=\vbox{\unvcopy\mdf@splitbox@save}%
\splitmaxdepth\z@ \splittopskip\mdf@splittopskip@length%
\mdf@ignorevbadness%
\setbox\mdf@splitbox@two\vsplit\mdf@splitbox@one to \dimen@i\relax%
\setbox\mdf@splitbox@two\vbox{\unvbox\mdf@splitbox@two}%
\setbox\mdf@splitbox@one\vbox{\unvbox\mdf@splitbox@one}%
\repeat%
}{}%
\ifvoid\mdf@splitbox@one\relax%
\mdf@PackageWarning{You got a bad break because the splittet box is
empty^^J
You have to change the page settings^^J
like enlargethispage or something else^^J
the package increases do
\enlargethispage{\baselineskip}\MessageBreak}%
\setbox\mdf@splitbox@one=\vbox{\unvcopy\mdf@splitbox@save}%
\enlargethispage{\baselineskip}%
\def\mdf@reserved@a{\mdf@put@frame@ii}%
\else
\setbox\mdf@splitbox@two=\vbox%
{%
\hrule \@height\z@ \@width\mdfboundingboxwidth\relax%
\unvcopy\mdf@splitbox@two%
}%
\begingroup%
\mdf@@setzref%
\booltrue{mdfmiddleframe}%
\mdf@beforebreak%
\mdf@putbox@middle%
\mdf@afterbreak%
\endgroup%
\hrule \@height\z@ \@width\hsize%
\vfill\eject%
\def\mdf@reserved@a{\mdf@put@frame@ii}%
\fi
}%End middle box case
{%start last box case
\ifvoid\mdf@splitbox@one
\mdf@PackageWarning{You got a bad break\MessageBreak
because the last split box is empty\MessageBreak
You have to change the settings1}%%
%CHANGE: leave final box as void
\iffalse
\setbox\mdf@splitbox@one=\vbox%
{%
\unvbox\mdf@splitbox@one%
\hrule \@height\z@ \@width\mdfboundingboxwidth
}%
\fi
%end CHANGE
\fi%
\ifdimless{\ht\mdf@splitbox@one}{1sp}%
{%
\mdf@PackageWarning{You got a bad break\MessageBreak
because the last split box is empty\MessageBreak
You have to change the settings2}%
\let\mdf@reserved@a\relax%
%CHANGE: add discard final box
\iffalse
\setbox\mdf@splitbox@one=\vbox%
{%
\unvbox\mdf@splitbox@one%
\hrule \@height\z@ \@width\mdfboundingboxwidth
}%
\fi
%END CHANGE
\setbox\mdf@splitbox@one\box\voidb@x
}{}%
\begingroup%
\toggletrue{mdflastframe}%
\mdf@beforebreak%
\begingroup%
\mdf@@setzref%
\booltrue{mdflastframe}%
\mdf@beforelastframe%
\mdf@putbox@second%
\mdf@afterlastframe%
\endgroup%
\hrule \@height\z@ \@width\hsize%
\mdf@afterbreak%
\endgroup%
\let\mdf@reserved@a\relax%
}%
\mdf@reserved@a%
}
\makeatother
\newmdenv[
usetwoside=false,
skipabove=3pt minus 1pt plus 3pt,
skipbelow=3pt minus 1pt plus 3pt,
leftmargin=-4pt,
rightmargin=-4pt,
innerleftmargin=2pt,
innerrightmargin=2pt,
innertopmargin=4pt,
innerbottommargin=4pt,
backgroundcolor=\boxcolor!20,
topline=false,
bottomline=false,
linecolor=\boxcolor,
linewidth=2pt,
]{aux*}
\newenvironment{mybox} {\begin{aux*}} {\end{aux*}}
\begin{document}
Mix text and equation to insert lots of glue
\begin{equation}\frac{a}{b}\end{equation}
Mix text and equation to insert lots of glue
\begin{equation}\frac{a}{b}\end{equation}
Mix text and equation to insert lots of glue
\begin{equation}\frac{a}{b}\end{equation}
Mix text and equation to insert lots of glue
\begin{equation}\frac{a}{b}\end{equation}
Mix text and equation to insert lots of glue
\begin{equation}\frac{a}{b}\end{equation}
Mix text and equation to insert lots of glue
\begin{equation}\frac{a}{b}\end{equation}
Mix text and equation to insert lots of glue
\begin{equation}\frac{a}{b}\end{equation}
and now the problematic box
\def\boxcolor{green}
\begin{mybox}%
\begin{equation}\label{Edwba}
\sum
\end{equation}%
\end{mybox}
See just above the nonsensical line produced by mdframed!
\begin{equation}ab\end{equation}
Mix text and equation to insert lots of glue
\begin{equation}\frac{a}{b}\end{equation}
Mix text and equation to insert lots of glue
\begin{equation}\frac{a}{b}\end{equation}
Mix text and equation to insert lots of glue
\begin{equation}\frac{a}{b}\end{equation}
Mix text and equation to insert lots of glue
\begin{equation}\frac{a}{b}\end{equation}
Mix text and equation to insert lots of glue
\begin{equation}ab\end{equation}
Mix text and equation to insert lots of glue
\begin{equation}ab\end{equation}
\begin{equation}ab\end{equation}
\def\boxcolor{red}
\begin{mybox}%
Here comes an example with three lines of text in the box.
Three lines is a lot of text bla bla bla bla bla bla blaaa.
Three lines is a lot of text bla bla bla bla bla bla blaaa.
\end{mybox}
See again the scandalous page break.
\end{document}
equationa new line starts. Can you use the box insideequation? – Sigur May 01 '15 at 10:59myboxcontains text. Hence the equation environment definitively has nothing to do with the problem. Maybe I should have chosen a text example to present my question in simpler form. – Joachim W May 01 '15 at 11:17Package mdframed Warning: You got a bad break (mdframed) because the last split box is empty– David Carlisle May 01 '15 at 13:17