Hi.You must define element style like this :
<DataGridTextColumn.ElementStyle>
<Style TargetType="{x:Type TextBox}">
<Style.Triggers>
<DataTrigger Binding="{Binding Subject}" Value="{x:Null}">
<Setter Property="Width" TargetName="NameDataGridColumn" Value="0"/>
</DataTrigger>
</Style.Triggers>
</Style>
</DataGridTextColumn.ElementStyle>
and also you must set Header="". I hope this solution help you.
Good Luck