why don't you use a hash to store shouldexist so you can delete by name?
something like

%shouldexist = (
'filename1' => 1,
..
'filenamen' => 1
);
#or just
%shouldexist = map {$_ => 1} @shouldexist;
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so you can simply do

for(@doexist) {
  delete $shouldexist{$_};
}
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if you whant to do the same using an array you have to scan @shouldexist on each iteration and delete when match (slower)