WPF TextBox Border when selected?

just see is this you want...

<Style x:Key="TextBoxStyle1" BasedOn="{x:Null}" TargetType="{x:Type TextBox}">        <Setter Property="BorderThickness" Value="1"/>        <Setter Property="Padding" Value="1"/>        <Setter Property="AllowDrop" Value="true"/>        <Setter Property="FocusVisualStyle" Value="{x:Null}"/>        <Setter Property="Template">            <Setter.Value>                <ControlTemplate TargetType="{x:Type TextBox}">                <Border x:Name="bg" BorderBrush="#FF825E5E" BorderThickness="1">                        <ScrollViewer x:Name="PART_ContentHost" SnapsToDevicePixels="{TemplateBinding SnapsToDevicePixels}"/>                        </Border>                    <ControlTemplate.Triggers>                        <Trigger Property="IsMouseOver" Value="True">                            <Setter Property="BorderBrush" TargetName="bg" Value="DarkBlue"/>                            <Setter Property="BorderThickness" TargetName="bg" Value="2"/>                        </Trigger>                        <Trigger Property="IsFocused" Value="True">                            <Setter Property="BorderBrush" TargetName="bg" Value="DarkBlue"/>                            <Setter Property="BorderThickness" TargetName="bg" Value="2"/>                        </Trigger>                    </ControlTemplate.Triggers>                </ControlTemplate>            </Setter.Value>        </Setter>    </Style> 

I think your problem is due to having the Trigger Property value containing TextBox. You just need the name of the property.

    <Style x:Key="ReadOnlyLargeTextBox" TargetType="{x:Type TextBox}">        <Setter Property="Height" Value="80"/>        <Setter Property="MaxHeight" Value="80"/>        <Setter Property="VerticalScrollBarVisibility" Value="Visible"/>        <Style.Triggers>            <Trigger Property="IsFocused"  Value="True">                <Setter Property="BorderBrush" Value="Blue"/>                <Setter Property="BorderThickness" Value="1"/>            </Trigger>            <Trigger Property="IsMouseOver" Value="True">                <Setter Property="BorderBrush" Value="Blue"/>                <Setter Property="BorderThickness" Value="1"/>            </Trigger>        </Style.Triggers>    </Style>

Check FocusVisualStyle property of the FrameworkElement object (ancestor of TextBox). It's purpose is to define style applied when an element is selected.