using System.Windows;
using System.Windows.Controls;

namespace WorkInstructionManager.Libs.Extend.System.Windows.Controls
{
    class AutoInputTextBox : TextBox
    {
        /// <summary>
        /// 入力完了時に操作するTarget要素を指定するプロパティ
        /// </summary>
        public static readonly DependencyProperty TargetProperty =
            DependencyProperty.Register("Target", typeof(UIElement), typeof(AutoInputTextBox), new PropertyMetadata(OnInitalizeTargetData));


        public AutoInputTextBox()
        {
            this.LostFocus += AutoInputTextBox_LostFocus;
        }


        /// <summary>
        /// 画面表示時にtargetのIsEnabledを更新します
        /// 基本falseになります
        /// </summary>
        /// <param name="d"></param>
        /// <param name="e"></param>
        private static void OnInitalizeTargetData(DependencyObject d, DependencyPropertyChangedEventArgs e)
        {
            var item = d as AutoInputTextBox;

            if (item.Target == null)
            {
                return;
            }
        }

        /// <summary>
        /// 対象のコントロール
        /// </summary>
        public UIElement Target
        {
            get
            {
                return (UIElement)GetValue(TargetProperty);
            }
            set
            {
                SetValue(TargetProperty, value);
            }
        }

        /// <summary>
        /// 自身のTextBoxのロストフォーカス時にTargetのTextBoxを処理します
        /// </summary>
        /// <param name="sender"></param>
        /// <param name="e"></param>
        private void AutoInputTextBox_LostFocus(object sender, RoutedEventArgs e)
        {
            if (Target == null || IsReadOnly) return;
            //ここの処理を変更でいろんなことできるかも
            ((TextBox)Target).Text = this.Text;
        }
    }
}

<Window x:Class="WpfApp1.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:WpfApp1"
        mc:Ignorable="d"
        Title="MainWindow" Height="350" Width="400">
    <Grid>
        <StackPanel VerticalAlignment="Center" HorizontalAlignment="Center">
            <Label Content="拡張TextBox"/>
            <local:AutoInputTextBox Target="{Binding ElementName=Test}" Width="150"/>
            <Label Content="対象のTextBox"/>
            <TextBox Name="Test" Width="150"/>
        </StackPanel>
    </Grid>
</Window>