_value is part of the type for Foo, it’s as if it was a public field. You can forge a reference to Foo by adding _value to your mock. TS deals with private fields by pretending they are public when it comes to matching. There are more rigorous ways have hiding and then revealing private state in structurally typed languages, but they involve something that is suspiciously like using a name, and really, it makes sense. The only way you can hide something and recover it later is via some kind of name (unless you can somehow capture the private structure in a type variable so it’s just passing through the parts that can’t see it).

You can do a lot just by hiding the private state and providing methods that operate on that private state in the type (using interfaces for example), but that approach doesn’t allow for binary methods (you need to reveal private state on a non-receiver in a method).

Can you explain the last part more? I don't think I'm grasping what you mean.