open(FH, "< $err_out") or die "can't open LOG FILE $!"; while (<FH>) { 
$last = $_;
} 
close FH;
print "Last line was: ", $last;

Alternatively you could just do this ad grab the whole file in an array:

open FH, $file or die $!;
@file = <FH>;
close FH;
print "Last 4 lines, backwards: ", @file[-1,-2,-3,-4];