possibly depending on an undocumented implementation detail of my version of Perl.

You most definitely are. The loop is suppose to take a list over which to iterate, but you're relying on the observable differences between that an the actual optimised implementation. You can see this by changing foreach (@arr) to what should be equivalent foreach ((),@arr).

Either iterate over the indexes

my @arr = qw/a b c/;
for (my $i=0; $i<@arr; ++$i) {
    my $e = $arr[$i];
    push @arr, 'd' if $e eq 'a';
    push @arr, 'e' if $e eq 'b';
    push @arr, 'f' if $e eq 'c';
    print $e;
}
print "\n";
[download]

Or use a queue

my @arr = qw/a b c/;
while (@arr) {
    my $e = shift(@arr);
    push @arr, 'd' if $e eq 'a';
    push @arr, 'e' if $e eq 'b';
    push @arr, 'f' if $e eq 'c';
    print $e;
}
print "\n";
[download]