In the back-end, create a module for the front-end side. The module type doesn't matter. Give it a name, for example "My Module".
Duplicate it with the "Duplicate" button in the top toolbar. The new module is automatically named "My Module (2)". Leave its name as is.
On both modules, ensure that the "Position" is "unset", or set it to a non-existing template position: we want to load the module through the content-loadmodule plugin, not through a standard template position. In addition ensure that the "Status" is "Published", and "Menu Assignment" to "All pages". These conditions are necessary for the content-loadmodule to load the module.
Create an article. Within its content load the module using the content-loadmodule plugin. To avoid struggling with the correct syntax, you can use the "Module" editor button introduced recently. There select "My Module (2)" from the list by the green button, which corresponds to {loadmodule}. Do not use the yellow button, which would correspond to {loadposition}.
Take a look to your module in the front-end. I created a Menu Item of type "Articles » Single Article" for that purpose, but browsing your article through a blog view should make no difference.
You should see that the plugin code has not been replaced with the actual module. The plugin seems not working at all.
Summary of Changes
The problem is that loadmodule calls preg_replace using a literal string as pattern, while in a regular expression the parenthesis are metacharacters and must be escaped.
Frankly, I would suggest to change preg_replace with str_replace, but I've just escaped the parenthesis to fix this bug without opening a debate.
I have follow above steps and not able to re-produce this issue in latest staging branch.
Joomla! Version: Joomla! 3.6.0-rc Release Candidate [ Noether ] 28-June-2016 20:34 GMT
With PR and without PR the module is being loaded fine in my article at front end site.
I have follow your testing instructions but not able to reproduce this issue in latest version of Joomla with applied patch and without applying patch.
I have used code to load the module in article which was "{loadmodule mod_articles_archive}".
I have noticed that it was loading original module not the copied module both module name were same in database "mod_articles_archive" so, not able to load copied module. If we used title of module then it was not replaced at front site, it was simple test for article.
Well spotted. Regular expressions can be rather slow so I agree that str_replace would be preferable.