From your description I'm making a few assumptions:
1. You have a directory that periodically has some workbooks placed in it
with updated data.
2. Each time the updated files are placed in the directory they have the
same names as they did previously.
3. When the data gets out of date, the source files are deleted from the
directory.

If my assumptions are correct, you may be able to get the effect that you're
after by creating a dummy set of source files which are all blank and each
time that you want to delete a set of "out of date" files, simply overwrite
them with the blank dummy set.
Next step is to change the update link settings in your dependant file(s) to
force an update whenever they're opened => references to blanks.
You may need to adjust the formulas in the dependant file(s) to cope with
the sudden appearance of the blanks where regular data is expected.

Rgds,
ScottO