How do I wrap a constructor?

I have this JavaScript:

var Type = function(name) {
    this.name = name;
};

var t = new Type();

Now I want to add this:

var wrap = function(cls) {
    // ... wrap constructor of Type ...
    this.extraField = 1;
};

So I can do:

wrap(Type);
var t = new Type();

assertEquals(1, t.extraField);

[EDIT] I'd like an instance property, not a class (static/shared) property.

The code executed in the wrapper function should work as if I had pasted it into the real constructor.

The type of Type should not change.