Use git show :path/to/some/file.
Files that are "staged" represent an index copy of the file that differs from some other copy, such as the current commit copy that you can access via HEAD:path/to/some/file.
Files that are stored in the index have a stage number, usually zero. (Staging slots 1, 2, and 3 are used during conflicted merges.)
To refer to the copy of the file named F (in your case F = path/to/some/file), use the revision specifier :number:F. In this case that's :0:path/to/some/file. When the number is zero—which it usually is—you can omit one colon and the zero, leaving :path/to/some/file.
Note that when git status says nothing about that file, it's in the index, it's just that :0:path/to/some/file has the same data as HEAD:path/to/some/file. If the file weren't in the index at all–in no staging slots—git status would tell you that the file is staged for deletion.
(Re the context: if you have space, I'd recommend doing a git checkout-index of every stage-zero-index-file into a temporary work area. To easily test whether all index files are at stage zero, use git write-tree, which fails if any files are in staging slots other than zero.)