try

my $string = '"foo"';
my $string2 = '"foo';
   $string =~ s/\"(.*?)\"|\"(.*?)/$1$2/;
   $string2 =~ s/\"(.*?)\"|\"(.*?)/$1$2/;
print "$string -- $string2\n";
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I think in the $string =~ s/\"(.*?)\"?/$1/; version both the .*? and the \"? are non-gready, so it's a question of which one is less gready competing, and \"? wins becuas it's non -greedy.

Updated:Corrected my muddle-headedness about "non-greedy ", thanks to betterwold.