Close Window on Deactivated and Focus on Parent Window WPF

You can do something like this for your desired result.

MainWindow.xaml

<Window x:Class="StackOverflow.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:StackOverflow"
        mc:Ignorable="d"
        Title="MainWindow" Height="450" Width="800">
    <Grid>
        <Button Height="50" Width="100" Content="Open Child" Click="Button_Click"/>
    </Grid>

MainWindow.xaml.cs

using System.Windows;

namespace StackOverflow
{
    public partial class MainWindow : Window
    {
        private Window _child;

        public MainWindow()
        {
            InitializeComponent();
            _child = new Window();
            _child.LostKeyboardFocus += _child_LostFocus;
        }

        private void _child_LostFocus(object sender, RoutedEventArgs e)
        {
            _child.Hide();
        }

        private void Button_Click(object sender, RoutedEventArgs e)
        {
            _child.Show();
        }
    }
}