<Grid>
        <StackPanel>
            <TextBox  x:Name="textBox"  GotFocus="textBox_GotFocus" />

            <Button Content="Button" Click="Button_Click"/>

            <Popup x:Name="popup" Width="100" Height="100" PlacementTarget="{Binding ElementName=textBox}" Placement="Bottom"
            StaysOpen="{Binding ElementName=text,Path=IsKeyboardFocused}" >
                <Grid Background="Blue">

                </Grid>
            </Popup>
            

        </StackPanel>
    </Grid>

        private void Button_Click(object sender, RoutedEventArgs e)
        {
            popup.IsOpen = false;
        }

        private void textBox_GotFocus(object sender, RoutedEventArgs e)
        {
            popup.IsOpen = true;
        }