Define "3rd party FTP program".
Do you mean when some (any) [S]FTP client
program uses [S]FTP to delete a file on your
[S]FTP server system? And what might that
system be?
uname -a
ssh -V
Any unusual FTP server, or the usual one?
FTP and SFTP are very different. Knowing
nothing, I'd guess that the usual FTP server
transfer log (if enabled) might record file
deletions. It should also be possible to
prohibit delete operations in at least a
couple of ways (FTP server configuration,
file permissions/ACLs). I know even less
about SFTP.
Is there some actual problem which you are
trying to solve?