How to create a type in TypeScript which can be a class or a function?

Question

I thought this could be accomplished like this:

abstract class Stuff() {
}
class Foox extends Stuff {
    constructor() {

    }
}
type Func = {
    (a: number): number
}

let y: Func | Stuff;

y = (a = 1) => { return a }
y = Foox;

new y(); // doesn't work. This expression is not constructable. Type 'Foox' has no construct signatures

This works:

y = (a: 1) => { return a }
y = new Foox();

but this is not what I want. I want to create a value which is either a function with a specific signature or a class, not the instance of the class. How can I do this?

EDIT:

Sorry, my question wasn't entirely precise. This is what I need:

abstract class Stuff {
}
class Foox extends Stuff {
    constructor() {
        super();
    }
}
type Func = {
    (a: number): number
}

let y: Func | Foox;

y = (a = 1) => { return a }
y = Foox;

new y(); // doesn't work. This expression is not constructable. Type 'Foox' has no construct signatures

So even this doesn't work. But I don't even know the name of the subclass. All I know if that it extends the abstract class Stuff. And I would like to create type:

Function | subclass of Stuff.

EDIT 2:

Managed to make it work thanks for the suggestions guys!

let y: Func | typeof Stuff;

works. Well, kinda. I'm still getting a warning, but it's OK.

And the code that checks which type it is is just:

if(y instanceof Stuff.prototype) {
}