How to switch per-chapter numbering to continuous numbering after a \chapter*{}?

Question

How can I switch per-chapter numbering inside float elements to continuous numbering and avoiding the chapter number inside sectioning elements (section, subsection, etc) after a \chapter*{} declaration in a book?

I need a numbering like this:

CHAPTER 1
1.1 Section
1.1.1 Subsection
Figure 1.1

UNNUMBERED CHAPTER
1 Section
1.1 Subsection
Figure 1

I need this only for one unnumbered chapter inside the book, not for all of them. The reason is that I need a unnumbered section (with a chapter level) followed by numbered sections and floats without the previous chapter number. So required by document layout rules.

Answer 1

Probably the easiest way is to change manually in proper places the behaviour of sections, as in the following example. If, in the example, the next chapter after unnumbered had to have number 3, one should uncomment \stepcounter{chapter}. If figures and tables are needed, please add also changes from egreg's comment.

\documentclass{report}

\begin{document}

\chapter{First}

\section{first}

\section{second}

\setcounter{section}{0}
\renewcommand{\thesection}{\arabic{section}}
\chapter*{Unnumbered}

\section{first}

\section{second}

\renewcommand{\thesection}{\thechapter.\arabic{section}}
%\stepcounter{chapter}
\chapter{Second?}

\section{first}

\section{second}

\end{document}