Я попробовал, и он устанавливает новую границу над границей сетки:
<Window x:Class="Class.Window"
xmlns="http://schemas.microsoft.com/winfx/2006/xaml/presentation"
xmlns:x="http://schemas.microsoft.com/winfx/2006/xaml"
Title="Window1" Width="379" Loaded="Window_Loaded"
AllowsTransparency="True"
ResizeMode="NoResize" ShowInTaskbar="False" Topmost="True" WindowStyle="None" Height="110">
<Border BorderBrush="Black" BorderThickness="1,1,1,1" CornerRadius="30,30,30,30">
<Grid>
<TextBlock Height="23" HorizontalAlignment="Left" Margin="62,12,0,0" Name="textBlock_From" Text="" VerticalAlignment="Top" Width="283" />
<TextBlock Height="23" HorizontalAlignment="Left" Margin="62,38,0,0" Name="textBlock_Subject" Text="" VerticalAlignment="Top" Width="283"
MouseLeftButtonDown="textBlock_Subject_MouseLeftButtonDown" MouseEnter="textBlock_Subject_MouseEnter" MouseLeave="textBlock_Subject_MouseLeave" />
</Grid>
</Border>
</Window>