<TreeView Width="100">
    <TreeViewItem>
        <Grid>
            <Grid.ColumnDefinitions>
                <ColumnDefinition Width="{Binding RelativeSource={RelativeSource AncestorType=TreeView}, Path=ActualWidth}"/>
            </Grid.ColumnDefinitions>
            <Grid.RowDefinitions>
                <RowDefinition/>
                <RowDefinition/>
            </Grid.RowDefinitions>
            <TextBlock Text="Lorem Ipsum" />
            <TextBlock Text="Lorem Ipsum is simply dummy text of the printing and typesetting industry. Lorem Ipsum has been the industry's standard dummy text ever since the 1500s, when an unknown printer took a galley of type and scrambled it to make a type specimen book."
                       TextWrapping="Wrap" Grid.Row="1"/>
            </Grid>
        </TreeViewItem>
    </TreeView>

width = actual_width_of_tree_view - relative_horizontal_offset_of_item

public static Double GetProjectTitleWidth(DependencyObject obj)
    {
        return (Double)obj.GetValue(ProjectTitleWidthProperty);
    }

    public static void SetProjectTitleWidth(DependencyObject obj, Double value)
    {
        obj.SetValue(ProjectTitleWidthProperty, value);
    }

    public static readonly DependencyProperty ProjectTitleWidthProperty = DependencyProperty.RegisterAttached(
        "ProjectTitleWidth",
        typeof(Double),
        typeof(DatawareSearchView),
        new UIPropertyMetadata(0.0, ProjectTitleWidthChanged));

    private static void ProjectTitleWidthChanged(DependencyObject d, DependencyPropertyChangedEventArgs e)
    {
        var targetElement = d as FrameworkElement;
        if (targetElement != null)
        {
            var bindingExpr = targetElement.GetBindingExpression(ProjectTitleWidthProperty);
            var sourceElement = bindingExpr.DataItem as FrameworkElement;
            if (sourceElement != null)
            {
                // calculating relative offset
                var leftTop = targetElement.TranslatePoint(new Point(0.0, 0.0), sourceElement);

                // trying to find ScrollViewer
                var border = VisualTreeHelper.GetChild(sourceElement, 0);
                if (border != null)
                {
                    var scrollViewer = VisualTreeHelper.GetChild(border, 0) as ScrollViewer;
                    if (scrollViewer != null)
                    {
                        // setting width of target element
                        targetElement.Width = scrollViewer.ViewportWidth - leftTop.X;
                    }
                }
            }
        }
    }

<Grid>
    <Grid.RowDefinitions>
        <RowDefinition Height="Auto"/>
        <RowDefinition Height="*" />
    </Grid.RowDefinitions>

    <TextBlock Text="{Binding Model.Code}" FontWeight="DemiBold" />
    <TextBlock Text="{Binding Model.Title}" TextWrapping="Wrap" Foreground="Gray" x:Name="tbTitle" Grid.Row="1"
               localviews:DatawareSearchView.ProjectTitleWidth="{Binding RelativeSource={RelativeSource AncestorType=TreeView}, Path=ActualWidth}"/>
</Grid>

<TextBlock Text="{Binding Model.Title}" Width="{Binding ActualWidth,
      ElementName=tvDatawareObjects}" TextWrapping="Wrap" Foreground="Gray" Grid.Row="1"/>