inodes ? hmm is this file opened by the process. or are you only redirecting the output of the process to this file. Looking at your scenario, i bliv it is the process who opens this file for writing. if the process creates it, then deleting should stop adding to the log, unless your program handles creation of the file again, while logging. So if you want this to stop, then your logging should have a logic not to recreate a file if it doesnt find one.
second, if the logging fails, the process should also close the log file descriptor. which if left open may recreate the file and write. ( it depends mostly on ur process, how it handles this log file)
if you are simply redirecting the log to the file, one way to stop logging is chmod and chown of this log file so that there are no write permissions on this file. the process ll stop logging into it further (and probably may even crash
)