In the following example I am using the command \vsplit. I can't see the reason why \vsplit produced an overfull \vbox
\documentclass{article}
\parindent0pt
\def\exampletext{Text Text Text Text Text Text Text Text Text Text Text Text
Text Text Text Text Text Text Text Text Text Text Text Text Text Text Text Text
Text Text Text Text Text Text Text Text Text Text Text Text Text Text Text Text }
\fboxsep=0pt
\fboxrule=1pt
\hfuzz=\maxdimen
\begin{document}
\setbox1=\vbox{
\hsize=8cm
\bfseries\huge\exampletext}
\boxmaxdepth0pt
\setbox0\vsplit1to2cm
\setbox0=\vbox{\unvbox0}
\fbox{\box0}
\fbox{\box1}
\end{document}
I used \hfuzz=\maxdimen to avoid overfull hbox in this example.