The system calls will return nonzero if they fail, so a construction like,     (my $res = system @args) and unlink $to_delete; will work. The return value is kept in $res in case you want to do something more about it.

Update: Ok, here's a fancier version

UFILE: while (@files) {
    #...
    system @args and do {
        unlink $to_delete;
        print LOG "'system @args' failed: ", $?;
        next UFILE;
    };
    system @other_args and
        print LOG "'system @other_args' failed: ", $?;
    #...
}
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After Compline,
Zaxo