Obviously it is not OS9 to blame but the way you copied the files from the OS9 Mac. Did you use some non-Mac filessystem to store the files in some step? If yes, then it was that step that disassembled the data+resource fork file into an Apple Double format with separate files.
Now, stripping the resource for off is usually OK IF you are handling pure cross-platform data files (.doc, .jpg, .dv etc). The Mac apps sometimes store some info in the resource fork but usually it is not important and can be re-created (preview thumbnails etc).
But some files like applications will corrupt if the lose their resource fork, even into a separate file.
So: it is best to use Mac-formatted volumes (a Mac share on a Windows network works too) to move Mac specific files. Another option is to wrap them into a container that will protect them in a non-Mac formatted volume. Compressing them with Mac utilities to a .sit, .sitx, .zip etc file does that. Mac OS X compresses .zip files with the resource fork intact.