EOF is simply C++'s way of telling you there is no more data. There's no EOF "character" that you can use to check if the file is completely written.
The way this is typically accomplished is to transfer the file over with one name, i.e. myfile.txt.transferring, and once the transfer is complete, move the file on the target host (back to something like myfile.txt). You could do the same by using separate directories.
In C, and I think it's the same in C++, EOF is not a character; it is a condition a file is (or is not) in. Just like media removed or network down is not a character.
All finite files have an end. If a file is being written by one process, and (assuming the OS allows it) simultaneously read (faster than it is being written) by another process,then the reading process will see an EOF when it has read all the characters that have been written.
What would probably work better is, if you can determine a length of time during which you can guarantee that you'll receive a significant number of bytes and write them to a file (beware OS buffering), then you can walk the directory once per period, and any file that has changed its file size can be considered to be unfinished.
Another approach would require OS support: check what files are open by the receiving process, with a tool like lsof. Any file open by the receiver is unfinished.
Neither C nor C++ have a standard way to determine if the file is still open for writing by another process. We have a similar situation: a server that sends us files and we have to pick them up and handle as soon as possible. For that we use Linux's inotify subsystem, with a watch configured for IN_CLOSE_WRITE events (file was closed after having been opened for writing), which is wrapped in boost::asio::posix::stream_descriptor for convenient asynchronicity.
Depending on the OS, you may have a similar facility. Or just lsof as already suggested.