Procedural:
Sending applications touches a "flag" file in the same directory.
When "filea.cmp" exists, "filea.txt" is complete.

UPDATE: I have no control over the file name and I cannot ask them to send an md5 or other file size/md5sum info.
If the sender can/will not tell you when the file is complete, you can only *assume* the state based on the lack of updates over a certain time period. If the sender is concerned that the information is complete when processed, they will provide a mechanism to do so.