Windowを継承してIsOpenプロパティを実装したWindowExを作成する

    public class WindowEx : Window
    {
        public static readonly DependencyProperty IsOpenProperty = DependencyProperty.Register(
            "IsOpen", typeof(bool), typeof(WindowEx), new PropertyMetadata(default(bool)));

        public bool IsOpen
        {
            get { return (bool)GetValue(IsOpenProperty); }
            set { }
        }

        protected override void OnContentRendered(EventArgs e)
        {
            base.OnContentRendered(e);
            SetValue(IsOpenProperty, true);
        }

        protected override void OnClosed(EventArgs e)
        {
            base.OnClosed(e);
            SetValue(IsOpenProperty, false);
        }
    }

Windowの継承元はWindowExに置き換えるてIsOepnプロパティをBind設定する

    public partial class MainWindow : WindowEx
    {
        public MainWindow()
        {
            InitializeComponent();       
            
        }        
    }

<local:WindowEx x:Class="WpfApplication1.MainWindow"
        xmlns="http://schemas.microsoft.com/winfx/2006/xaml/presentation"
        xmlns:x="http://schemas.microsoft.com/winfx/2006/xaml"
        xmlns:d="http://schemas.microsoft.com/expression/blend/2008"
        xmlns:mc="http://schemas.openxmlformats.org/markup-compatibility/2006"
        xmlns:local="clr-namespace:WpfApplication1"
        mc:Ignorable="d" IsOpen="{Binding IsOpen.Value , Mode=OneWayToSource}"
        Title="MainWindow" Height="350" Width="525">
    <Window.DataContext>
        <local:MainWindowViewModel />
    </Window.DataContext>
    <Grid>
        
    </Grid>
</local:WindowEx>

ViewModelクラス

    public class MainWindowViewModel
    {
        public MainWindowViewModel()
        {
            IsOpen.Subscribe(x =>
            {
                Debug.WriteLine(x);
            });
        }

        public ReactiveProperty<bool> IsOpen { get; set; } =
            new ReactiveProperty<bool>();
    }