You've already been shown how to make your code work with all values including undef.

while (@array) {
   my $item = shift(@array);
   print "$item\n";
}
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If you wanted safe code that didn't refer to the array twice, you could use splice in a list assignment.

while (my ($item) = splice(@array, 0, 1)) {
   print "$item\n";
}
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The parens on the LHS of the assignment are crucial to force a list context. The result of a list assignment in list context is the number of list elements assigned (no matter if the element(s) are true or false).