Any file can be placed in the 'Incomplete' folder on your computer. It is just a folder, after all. When you choose to view the 'Incomplete' folder in LimeWire, it will display every file it finds in that folder. If LimeWire does not have information about a particular file (the hash of the completed file and/or the range of bytes that have been downloaded for that file) then it will not consider it an 'incomplete' file and will display it in red.

The downloads.dat (downloads.bak just being an automated backup of downloads.dat, should it become corrupt in any way) file is essentialy a map that keeps track of filenames, and for each filename it points to the completed hash & range of downloaded bytes for that file.

downloads.dat is the only way LimeWire can keep track of what files it is currently downloading, and how far along those downloads have progressed. If it is missing information or is malformed, then LimeWire won't be able to re-start old downloads. This will lead to LimeWire saying, "Sorry, but LimeWire was unable to restart your old downloads." when LimeWire starts.