There are at least two parts to every saved Audacity Project. There is the .AUP file and there is a data folder.
For example if you save a project as "mysong", then Audacity will create a file called "mysong.aup" and a data folder called "mysong_data".
The data folder contains the actual audio data that is used in the project and the .AUP file contains a list of instructions that tell Audacity what to do with the data. The .AUP file does not contain any data. (see here for more information:
http://wiki.audacityteam.org/index.php? ... ement_Tips )
There may also be audio data used in the project that is not in the data folder. If you import an uncompressed audio file (such as a WAV file) into Audacity, then by default Audacity will not copy the file into the data folder. Because Audacity is not copying it the file can open more quickly and it saves on disk space (which can be very useful if working with large files). Such files are called "dependencies" (because the project depends on them).
If you attempt to open a .AUP file and some of the audio data is unavailable you will get an error message such as the errors that you are seeing. This can occur because the data folder has been renamed or deleted, or a dependant file is unavailable because it has been renamed or deleted, or the .AUP file or the data folder have been moved to a different directory.
You can resolve the problem of dependencies by going to "Edit menu > Preferences > File Formats" and select the option "Make a copy of the file before editing (safer)".
The advice regarding the .AUP file and data folder is do not move them, do not delete them, do not rename them, do not manually change them in any way.
To avoid loosing work (for whatever reason) it is thoroughly advised to Export back-up copies of the work as WAV files.
If they are making recordings (rather than working with imported audio) I would also recommend making a backup of the recorded track immediately after recording, then make another backup (with a different file name) after the project has been edited/mixed.