use strict;
use warnings;
use 5.010;

for (qw/'abc' "abc" 'abc"/) {
    if (/(?<FQ>['"])(?<content>(?:(?!\k<FQ>).)+)\k<FQ>/s) {
        say $+{content};
    }
    else {
        say "Not matched: $_";
    }
}
__END__
abc
abc
Not matched: 'abc"