There are of course a lot of ways to collapse a XAML TextBlock, but here is one using a style.
<TextBlock Text="{Binding Path=DescriptiveText}">
<TextBlock.Style>
<Style TargetType="TextBlock">
<Style.Triggers>
<Trigger Property="Text" Value="{x:Null}">
<Setter Property="Visibility" Value="Collapsed" />
</Trigger>
<Trigger Property="Text" Value="">
<Setter Property="Visibility" Value="Collapsed" />
</Trigger>
</Style.Triggers>
</Style>
</TextBlock.Style>
</TextBlock>
As always, feel free to comment, or ask.