I came up with my own solution and I am sharing it here since it might be useful to others.
Using tcolorbox, mdframed and similar packages is an option but first, I wanted to know how to do proper spacing, second the lines will not necessarily be in my final design, third they seemed an overkill (they use tikz) for what I needed.
So, I had a look at this question Environment with first paragraph in bold and no pagebreaksand realised that the way to go is setting penalties and widow/orphan values.So, in order to have a paragraph break that discourages page breaks and keeps the text together you can define something like:
\newcommand{\nbpar}{\widowpenalty=10000 \@@par\penalty10000}then my environment can be rewritten as
\newenvironment{example}[1][]{% \def\@extitle@{#1}% \refstepcounter{example}% \par\smallskip% {\parskip=0.5\baselineskip \advance\parskip by 0pt plus 0pt% \textbf{Example~\theexample{}}~{\color{gray}\filltoend}% \ifx\@extitle@\@empty\relax\else\nbpar\textbf{#1}\fi\nbpar\mbox{}}% \itshape\ignorespaces}% {\nbpar{\color{gray}\filltoend\mbox{}}}there I also redefined (in a group) \parskip so I can control how stretchable the space in the heading block is.
Now, since I did not really like how it looked, I settled for a simpler but yet, I think, nice way of setting apart the example from the rest of the content: bold heading, and an ornament at the end; using \nbpar as above to handle spacing.
\usepackage{adforn}\newcommand{\exOrnament}{\adforn{21}}\newenvironment{example}[1][]{% \def\@extitle@{#1}% \refstepcounter{example}% \par\medskip% {\parskip=0.5\baselineskip \advance\parskip by 0pt plus 0pt \textbf{Example~\theexample{}}% \ifx\@extitle@\@empty\relax\else~--~\textbf{#1}\fi\nbpar\makebox{}}% \itshape\ignorespaces}% {\unskip\nbpar\hfill\exOrnament\hfill\mbox{}\par}