Without my, Perl does not use the variable $S4 for the loop, but instead uses a new lexically variable also named $S4. Thats why the first variable $S4 is uninitialized in sub X.

So your code behaves like this:

#!env perl
use strict;
use warnings;

my $S4;

sub X {
    print "<$S4>\n";
    return $S4;
}

for my $other_variable_also_named_S4 (1 .. 2) {
    print "A: <$other_variable_also_named_S4> <", X(), ">\n";
}
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Conway warns to use this construct since its 'behaviour is contrary to all reasonable expectation'.

BTW: perlcritic warns about it too.