Try a style like this (I’ve added background colours to make the change obvious):
<Style TargetType="TextBox">
<Setter Property="Background" Value="Yellow" />
<Style.Triggers>
<DataTrigger Binding="{Binding IsKeyboardFocused, RelativeSource={RelativeSource Self}}" Value="false">
<Setter Property="Template">
<Setter.Value>
<ControlTemplate TargetType="TextBox">
<TextBlock Text="{TemplateBinding Text}" TextTrimming="CharacterEllipsis" Background="Red" />
</ControlTemplate>
</Setter.Value>
</Setter>
</DataTrigger>
</Style.Triggers>
</Style>