That doesn't deal with double backslashes properly. Consider:

    abc "a\"bc$xy\\z$abc$x­$y\\" $bla'h, "$baz"
    #                        ^^
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You might look at Regex::Common, but I suspect it might not be helpful. (:

In any case, here is how I'd solve it:

    $str =~ s[
        \G            # Don't skip anything
        (             # $1 is unquoted text
          (?:
            [^\\"]+   # Uninteresting stuff
          | \\.       # Escaped character
          )*
        )(            # $2 is quoted text
          "           # Opening quote 
          (?:
            [^\\"]+   # Unintersting stuff
          | \\.       # Escaped character
          )*
          ("?)        # $3 is closing quote
        )
    ][
        die "Unclosed quote ($2)"   unless  $3;
        my $q= $2;
        $q =~ s[\$][\\\$]g;
        $1 . $q;
    ]xseg;
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Updated to address Aristotle's point about escaped quotes outside of quoted strings, though that assumes that such is possible (it makes sense for a shell script but not for Perl code).

Also note that eyepopslikeamosquito now says that neither of these ever happen. Oh, well.

Update2: Thanks, eyepopslikeamosquito. Sorry I didn't get a chance to test the code and I'm glad you were able to figure out what was wrong with it.

Very nice solution! Your interpretation of quoting is correct (I blundered before). Your solution does not work, as is, however, because $1 gets clobbered. The following minor changed version of your solution does work for me (note also the extra line of test data with your quoting example).

my $str = <<'EOS';
abc "a\"bc$xyz$abc$x$y" $bla'h, $blah
hello k\$nob
this is "\"'abc$xy$z\"" test "$"
a$$bc "$$abc$xyz$abc$" blah, $$, blah
abc "a\"bc$xy\\z$abc$x$y\\" $bla'h, "$baz"
EOS
print "$str\n\n";

    $str =~ s[
        \G            # Don't skip anything
        (             # $1 is unquoted text
          (?:
            [^\\"]+   # Uninteresting stuff
          | \\.       # Escaped character
          )*
        )(            # $2 is quoted text
          "           # Opening quote 
          (?:
            [^\\"]+   # Unintersting stuff
          | \\.       # Escaped character
          )*
          ("?)        # $3 is closing quote
        )
    ][
        die "Unclosed quote ($2)"   unless  $3;
        my $t = $1;   # changed line
        my $q = $2;
        $q =~ s[\$][\\\$]g;
        $t . $q;      # changed line
    ]xseg;
print $str;
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which prints:

abc "a\"bc$xyz$abc$x$y" $bla'h, $blah
hello k\$nob
this is "\"'abc$xy$z\"" test "$"
a$$bc "$$abc$xyz$abc$" blah, $$, blah
abc "a\"bc$xy\\z$abc$x$y\\" $bla'h, "$baz"


abc "a\"bc\$xyz\$abc\$x\$y" $bla'h, $blah
hello k\$nob
this is "\"'abc\$xy\$z\"" test "\$"
a$$bc "\$\$abc\$xyz\$abc\$" blah, $$, blah
abc "a\"bc\$xy\\z\$abc\$x\$y\\" $bla'h, "\$baz"
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as does my original attempt; however, the last line of this new test data trips up the earlier one liner.

local $_ = q[abc \"$a"bc$xyz$abc$x$y" $bla'h];
s/("(\\\"|[^"])+")/{$_=$1;s|\$|\\\$|g;$_}/ge;
print;
__END__
abc \"\$a"bc$xyz$abc$x$y" $bla'h
[download]

Makeshifts last the longest.

Yep, that works for me. Thanks.