You do it like this:

foreach $log (@logfiles) {
         rename($log,$log.".tmp");
         ProcessLogfile($log.".tmp");
}

foreach $log (@logfiles) {
         del($log.".tmp");
};
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this way, everything that is logging, will keep on logging into it's open filedescriptor (ie - the new data will go into .tmp file).

The problem is - how long are your external logging processing keeping their logfile descriptors open, the key part being - are they keeping their descriptors opened indefinitely? Then you're out of luck and can't really do what you're trying to achieve.

If their logging method is

open(LOG,">>logfile");
print LOG "memo";
close LOG;
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then the method described above would work OK.