Csharp WeakReference未被垃圾收集

我的理解是，在对WeakReference的Target的所有强引用设置为空并调用GC之后，该弱引用应该不再有效.

然而，下面的代码似乎并不符合这一预期:

    static void Main(string[] _) {
        var person = new Person();
        var wr = new WeakReference(person);

        person = null;

        // We should have access to the person here
        if (wr.Target is Person shouldExist)
        {
            Console.WriteLine($"Person exists! IsAlive: {wr.IsAlive}.");
            shouldExist = null;
        }
        else
        {
            Console.WriteLine($"Person does not exist :( IsAlive: {wr.IsAlive}.");
        }

        // Invoke GC.Collect.            
        GC.Collect();


        if (wr.Target is Person shouldNotExist)
        {
            Console.WriteLine("This person should have been garbage collected");
            Console.WriteLine($"IsAlive: {wr.IsAlive}");
        }
        else
        {
            Console.WriteLine("This person was garbage collected and weak reference is no longer alive");
            Console.WriteLine($"IsAlive: {wr.IsAlive}");
        }
    }

哪里

class Person
{
    private int mI = 3;
    public int MI { get => mI; set => mI = value; }
}

输出结果是

Person exists! IsAlive: True. This person should have been garbage collected IsAlive: True个

我原以为输出为:

Person exists! IsAlive: True. This person was garbage collected and weak reference is no longer alive IsAlive: False个

我在这里错过了一些关于弱引用如何工作的东西吗？