What does `new $cur->{LINK}' do? (Assume the current package has no new() function of its own.)

$cur->new()->{LINK}
The indirect object syntax only has a single token lookahead. That means if new() is a method, it only grabs the very next token, not the entire following expression.
This is why `new $obj[23] arg' does't work, as well as why `print $fh[23] "stuff\n"' does't work. Mixing notations between the OO and IO notations is perilous. If you always use arrow syntax for method calls, and nothing else, you'll not be surprised.