why this throws exception ... my @b = @$a; ... and why this one works smoothly ... foreach (@$a) { }

I hope that my earlier explanations, about why my $x; my $y = @$x; throws an error but my $x; @$x = (); does not, make sense? Do you see how in the second example, @$x is in "lvalue context", that is, it is on the left-hand side of the assignment?

foreach is kind of special, it aliases the loop variable to the things it is looping over. In the following, see how $val becomes an alias for each of the variables in turn and the original values $x,$y,$z are modified via $val:

my ($x,$y,$z) = ('x','yy','zzz');
for my $val ($x,$y,$z) {
    $val = $val . length($val);
}
print "$x/$y/$z\n";  # prints "x1/yy2/zzz3"
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Loosely speaking, this is why the variables foreach (...) is looping over are treated by Perl as if they were on the left-hand side of an assignment (lvalue context), and why the autovivification behavior is applied to them.