I experimented with this as I added to enigma_engine.php self-encryption, if no valid key was found for the receiver.
So, I appended a message before the encrypted message, saying that, if he cannot read it (because he does not have the pgp key), he can click on a link which would decrypt the message, if he knows the password.

Now my sieve configuration broke and I am unable to test until I fix it again. But I saw that enigma was behaving correctly. The message was displayed before the decryption password was entered, followed by the ---PGP PART---. Once the password was entered, the message of course disappeared. Same behavior in enigmail.

For my use, I would mark this as resolved. If there is some other use, I don't know.

On Wed, Jan 27, 2016 at 10:00 AM, Roundcube Webmail <trac@roundcube.net> wrote:
#1490633: Enigma: Mail containing text + PGP encrypted part is not decrypted
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 Reporter:  devotedmystic  |       Owner:
     Type:  Bugs           |      Status:  new
 Priority:  3              |   Milestone:  1.2-RC
Component:  Plugins        |     Version:  1.2-beta
 Severity:  major          |  Resolution:
 Keywords:                 |
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Comment (by alec):

 I couldn't find any standard for this, but e.g. Enigmail can handle such
 messages (with warning that only part of the body was encrypted). So, we
 should support this too, I suppose.
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Ticket URL: <http://trac.roundcube.net/ticket/1490633#comment:4>
Roundcube Webmail <http://www.roundcube.net/>
Roundcube Webmail is a browser-based multilingual IMAP client with an application-like user interface. It provides full functionality you expect from an e-mail client, including MIME support, address book, spell checking, folder manipulation and plugins. Roundcube Webmail is written in PHP and requires a MySQL, Postgres, MSSql or SQlite database. The user interface is fully skinnable using HTML and CSS.