Place your matching regex in an if statement. If true, you can print your captures w/o error. The else can handle the exceptions:

use strict;
use warnings;

while (<DATA>) {
    next unless /^\d+\|(\d+?)\|/ and $1 == 1;
    
    if (/^(.*\|)*.*ABC\.pi=([\d.]+|[\w.]+)*.*ABC\.id=(\d+|[\w.]+).*$/)
+ {
        print "$1$2|$3\n";
    }
    else {
        print "Exception: $_";
    }
}
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Output on your data:

123|1|456464|645646|4546|112.33.44.55.66|789137136770
123|1|456464|645646|4546|112.33.44.55.67|789134713670
123|1|456464|645646|4546|112.33.44.55.68|789137213670
123|1|456464|645646|4546|112.33.44.55.69|78913713670
Exception: 123|1|456464|645646|4546|654~abc~dhghga~12.33.44.55.70~3713
+670
123|1|456464|645646|4546|112.33.44.55.70|78913713670
123|1|456464|645646|4546|112.33.44.55.70|78913713670
123|1|456464|645646|4546|112.33.44.55.70|789137135670
123|1|456464|645646|4546|112.33.44.55.70|789137153670
Exception: 123|1|456464|645646|4546|654~abc~dhghga~12.33.44.55.70~3713
+670
Exception: 123|1|456464|645646|4546|654~abc~dhghga~121322~456466874~87
+96896
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