Windows crops the edges of the window when it's maximized to obscure what would normally be the resize edges. You can get around this by putting a proxy border between the window and your content and then inflate the thickness when it's maximized.
I modified the example that came with the lib to do this, the same basic change could be made to your sample:
<ControlTemplate TargetType="{x:Type local:SelectableChromeWindow}">
<Border BorderBrush="Green">
<Border.Style>
<Style TargetType="{x:Type Border}">
<Setter Property="BorderThickness" Value="0"/>
<Style.Triggers>
<DataTrigger Binding="{Binding ElementName=ThisWindow, Path=WindowState}" Value="Maximized">
<Setter Property="BorderThickness" Value="{Binding Source={x:Static shell:SystemParameters2.Current}, Path=WindowResizeBorderThickness}"/>
</DataTrigger>
</Style.Triggers>
</Style>
</Border.Style>
<Grid [...]/>
</Border>
</ControlTemplate>
I hope that helps.
For .net 4.5 and above, the SystemParameters are a little different, e.g.:
<DataTrigger Binding="{Binding RelativeSource={RelativeSource AncestorType={x:Type local:MainWindow}}, Path=WindowState}" Value="Maximized">
<Setter Property="BorderThickness" Value="{Binding Source={x:Static SystemParameters.WindowResizeBorderThickness}}"/>
</DataTrigger>
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