The two aren't related. You can easily log something that doesn't happen every time:

use warnings;
use strict;
use Data::Dumper;
$Data::Dumper::Useqq=1;
my $count = 0;
for (1..100) {
    my $string = ("0\x04\x88\x80\x80\x80\x86\x98\x050", "7630001998")[
+ (rand()<0.1) ? 0 : 1 ];
    if($string =~ /[^0-9]/) {
        print STDERR "Warning, weird string #", ++$count, " on run #$_
+ at ", scalar localtime, ": ", Dumper($string);
    }
}

__END__
Warning, weird string #1 on run #7 at Wed Mar 11 08:59:53 2020: $VAR1 
+= "0\4\210\200\200\200\206\230\0050";
Warning, weird string #2 on run #16 at Wed Mar 11 08:59:53 2020: $VAR1
+ = "0\4\210\200\200\200\206\230\0050";
Warning, weird string #3 on run #30 at Wed Mar 11 08:59:53 2020: $VAR1
+ = "0\4\210\200\200\200\206\230\0050";
Warning, weird string #4 on run #36 at Wed Mar 11 08:59:53 2020: $VAR1
+ = "0\4\210\200\200\200\206\230\0050";
Warning, weird string #5 on run #37 at Wed Mar 11 08:59:53 2020: $VAR1
+ = "0\4\210\200\200\200\206\230\0050";
Warning, weird string #6 on run #46 at Wed Mar 11 08:59:53 2020: $VAR1
+ = "0\4\210\200\200\200\206\230\0050";
Warning, weird string #7 on run #54 at Wed Mar 11 08:59:53 2020: $VAR1
+ = "0\4\210\200\200\200\206\230\0050";
Warning, weird string #8 on run #60 at Wed Mar 11 08:59:53 2020: $VAR1
+ = "0\4\210\200\200\200\206\230\0050";
Warning, weird string #9 on run #71 at Wed Mar 11 08:59:53 2020: $VAR1
+ = "0\4\210\200\200\200\206\230\0050";
Warning, weird string #10 on run #95 at Wed Mar 11 08:59:53 2020: $VAR
+1 = "0\4\210\200\200\200\206\230\0050";
Warning, weird string #11 on run #96 at Wed Mar 11 08:59:53 2020: $VAR
+1 = "0\4\210\200\200\200\206\230\0050";
Warning, weird string #12 on run #98 at Wed Mar 11 08:59:53 2020: $VAR
+1 = "0\4\210\200\200\200\206\230\0050";
[download]

Notice the "weird" event happens only ~10% of the time, but it can datalog just fine. Use whatever logging system you have in place, rather than STDERR, in your application.