Enriched mode implements an extension command to the text/enriched
format called "x-display", which stores "display" text properties.
It was added awhile ago:

  commit d9e28c1ca1d95f51a05d052dcf1fe06888d52476
  Author: Gerd Moellmann <gerd@gnu.org>
  Date:   Wed Jul 21 21:43:03 1999 +0000

  (enriched-translations): Add `display' and "x-display".
  (enriched-handle-display-prop): New.
  (enriched-decode-display-prop): New.

It's possible to use this extension command to transparently execute
arbitrary code in an Emacs process that opens a text/enriched file.
For example, if you open a file containing the following contents:

Content-Type: text/enriched
Text-Width: 70

<x-display><param>(when (message "hello world") nil)</param>test</x-display>

Then "hello world" will be printed in the echo area whenever the
"test" text is displayed (which is immediate).  Note that the
s-expression between the <param> tags needs to conform to a "display"
spec: but since there are a few display specs that can execute code,
it's not difficult to craft a file that could have bad effects (shell
commands work, for example).  Additionally, such a file can be
compressed with gzip (thus hiding the contents), and when it is
opened, Emacs will automatically decompress it and apply the display
properties.  Attached is an example file (enriched-bug-example.txt)
that turns the mode line red as soon as you open it.  It works in
23.4, 24.5, 25.2 and master (and possibly earlier versions -- I
haven't tested).

Other extensions in `enriched-translations' of enriched.el may have
similar issues (I don't understand them all, so I hope somebody else
can make sure).