"Embed local media" works easily for images, oddly for files
Using Jamroom
The out-of-the-ordinary "Embed local media" item is the image upload, the files follows the normal pattern of every item belonging to a profile.
one of the core traits of jamroom is that the canonical location for everything is on a profile. The non-profile sections are just there to direct to a profile.
Think: Jamrooms origins are many bands uploading songs to their band profile. The songs belong to the band that uploaded them. Everything that band uploads is not the property of the site itself, but rather the bands profile on the site.
So if Tom uploads a file to his profile its Toms file.
When the Embed Local Media module got made it allowed the owner of the profile to embed their stuff from their profile into blog posts.
Then the jrUpImage module was made to add small images to the blogs that weren't part of the Gallery. But images uploaded via this method essentially disappear because they dont have a canonical location.
There is no module that exists to add files that do not have a canonical location.