One option is to catch WM_MOVING window message and manipulate its lParam. Since WM_MOVING comes before the Window moves, you can adjust the next position as you wish.
using System;
using System.Runtime.InteropServices;
using System.Windows;
using System.Windows.Interop;
public partial class MainWindow : Window
{
    private const int WM_MOVING = 0x0216;
    [StructLayout(LayoutKind.Sequential)]
    private struct RECT
    {
        public int left;
        public int top;
        public int right;
        public int bottom;
    }
    private int _left;
    private int _width;
    public MainWindow()
    {
        InitializeComponent();
        this.Loaded += OnLoaded;
    }
    private void OnLoaded(object sender, RoutedEventArgs e)
    {
        _left = (int)this.Left;
        _width = (int)this.Width;
        var handle = new WindowInteropHelper(this).Handle;
        var source = HwndSource.FromHwnd(handle);
        source.AddHook(new HwndSourceHook(WndProc));
    }
    private IntPtr WndProc(IntPtr hwnd, int msg, IntPtr wParam, IntPtr lParam, ref bool handled)
    {
        if (msg == WM_MOVING)
        {
            var position = Marshal.PtrToStructure<RECT>(lParam);
            position.left = _left;
            position.right = position.left + _width;
            Marshal.StructureToPtr(position, lParam, true);
        }
        return IntPtr.Zero;
    }
}