My original attempted answer worked fine for my development setup, but didn't work on our staged deployment setup, as for some reason it didn't include the XULRunner files inside the web package created using MSDeploy. I've found what seems to be a simpler setup, below:
<ItemGroup>
<Content Include="XULRunner\**\*.*">
<CopyToOutputDirectory>PreserveNewest</CopyToOutputDirectory>
</Content>
</ItemGroup>
I'm not 100% sure if this works universally, but it seems to work better in every development and deployment scheme I've encountered thus far.