Collecting exactly the dead objects in all situations is not possible even in theory:

    function f() {
        x = Object(1)
        if (halts(some_program)) {
            return Object(2)
        } else {
            return x;
        }
    }

The contents of x will be dead or not after the assignment depending on whether some_program halts. But a GC that could determine that could solve the halting problem.