To elaborate a bit (it took me some experimenting to realize why cfreak is right), inside a map the variable $_ is magic. While each entry in the list is evaluated, $_ is an alias to that entry. Assigning a new value to $_ changes the value of the current list entry. Because you're calling screwed from within map without localizing $_, it's being assigned to each successive line in the file, and then set to undef to indicate end-of-file. When screwed returns, $_ is still set to undef, so all entries in the list are changed to undef.

You can verify this by changing screwed to:

sub screwed {
  $_ = 'hi';
}
[download]

in which case you'll get:

before a
before b
after hi
after hi