gistfile1.cs

using System;
using System.Collections.Generic;
using System.Linq;
using System.Text;
using System.Threading.Tasks;
using System.Windows;
using System.Windows.Controls;
using System.Windows.Media;
using System.Windows.Threading;

namespace WpfApplication2
{
    public class CustomTextBox : TextBox
    {
        public override void OnApplyTemplate()
        {
            // call base method
            base.OnApplyTemplate();

            // override design
            var stackpanel = (StackPanel)GetTemplateChild("stackpanel");
            stackpanel.MouseDown += (sender, args) =>
            {
                SelectionStart = Text.Length;
                SelectionLength = 0;
            };
        }
        
    }
}

gistfile1.xaml

<Window x:Class="WpfApplication2.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:WpfApplication2"
        mc:Ignorable="d"
        Title="MainWindow" Height="350" Width="525">
    <Window.Resources>
        <SolidColorBrush x:Key="TextBox.Static.Border" Color="#FFABAdB3"/>
        <SolidColorBrush x:Key="TextBox.MouseOver.Border" Color="#FF7EB4EA"/>
        <SolidColorBrush x:Key="TextBox.Focus.Border" Color="#FF569DE5"/>
        <Style x:Key="TextBoxStyle1" TargetType="{x:Type TextBox}">
            <Setter Property="Background" Value="{DynamicResource {x:Static SystemColors.WindowBrushKey}}"/>
            <Setter Property="BorderBrush" Value="{StaticResource TextBox.Static.Border}"/>
            <Setter Property="Foreground" Value="{DynamicResource {x:Static SystemColors.ControlTextBrushKey}}"/>
            <Setter Property="BorderThickness" Value="1"/>
            <Setter Property="KeyboardNavigation.TabNavigation" Value="None"/>
            <Setter Property="HorizontalContentAlignment" Value="Left"/>
            <Setter Property="FocusVisualStyle" Value="{x:Null}"/>
            <Setter Property="AllowDrop" Value="true"/>
            <Setter Property="ScrollViewer.PanningMode" Value="VerticalFirst"/>
            <Setter Property="Stylus.IsFlicksEnabled" Value="False"/>
            <Setter Property="Template">
                <Setter.Value>
                    <ControlTemplate TargetType="{x:Type TextBox}">
                        <Border x:Name="border" BorderBrush="{TemplateBinding BorderBrush}" BorderThickness="{TemplateBinding BorderThickness}" Background="{TemplateBinding Background}" SnapsToDevicePixels="True">
                            <StackPanel Orientation="Horizontal" Cursor="IBeam" x:Name="stackpanel" Background="Transparent">
                                <ScrollViewer x:Name="PART_ContentHost" Focusable="false" HorizontalScrollBarVisibility="Hidden" VerticalScrollBarVisibility="Hidden" />
                                <TextBlock Text=".slack.com" IsHitTestVisible="False"/>
                            </StackPanel>
                        </Border>
                        <ControlTemplate.Triggers>
                            <Trigger Property="IsEnabled" Value="false">
                                <Setter Property="Opacity" TargetName="border" Value="0.56"/>
                            </Trigger>
                            <Trigger Property="IsMouseOver" Value="true">
                                <Setter Property="BorderBrush" TargetName="border" Value="{StaticResource TextBox.MouseOver.Border}"/>
                            </Trigger>
                            <Trigger Property="IsKeyboardFocused" Value="true">
                                <Setter Property="BorderBrush" TargetName="border" Value="{StaticResource TextBox.Focus.Border}"/>
                            </Trigger>
                        </ControlTemplate.Triggers>
                    </ControlTemplate>
                </Setter.Value>
            </Setter>
            <Style.Triggers>
                <MultiTrigger>
                    <MultiTrigger.Conditions>
                        <Condition Property="IsInactiveSelectionHighlightEnabled" Value="true"/>
                        <Condition Property="IsSelectionActive" Value="false"/>
                    </MultiTrigger.Conditions>
                    <Setter Property="SelectionBrush" Value="{DynamicResource {x:Static SystemColors.InactiveSelectionHighlightBrushKey}}"/>
                </MultiTrigger>
            </Style.Triggers>
        </Style>
    </Window.Resources>
    <Grid>
        <local:CustomTextBox VerticalAlignment="Center" Style="{StaticResource TextBoxStyle1}"/>
    </Grid>
</Window>