I get the same complaint, on the same line.

False positive. It apparently doesn't check for local $_. I tend to avoid local $_ anyway. What follows is a list of alternatives.

(Note that chomp is probably redundant with s/\+s$//;, so I omitted it.)

my @files = map { my $s = $_; $s =~ s/^\s+//; $s =~ s/\+s$//; $s }
            <$FILES>;
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my @files = map { my $s = $_; for ($s) { s/^\s+//; s/\+s$//; } $s }
            <$FILES>;
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my @files = <$FILES>;
for (@files) { s/^\s+//; s/\+s$//; }
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use List::MoreUtils qw( apply );
my @files = apply { s/^\s+//; s/\+s$//; } <$FILES>;
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use Algorithm::Loops qw( Filter );
my @files = Filter { s/^\s+//; s/\+s$//; } <$FILES>;
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Or turn off disable the critic for that instance, since you're only inadvertently modifying anonymous elements on the stack.

Do you need an array in the first place?

while (<$FILES>) {
   s/^\s+//; s/\+s$//;
   ...
}
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