The command is called Drape Curve...
and it projects a feature line to a grading grid.
The feature line stays linked to that grid so any modifications to it, directly or indirectly, will cause the feature line to update - the wish that has been granted...kind of (read on).
Now you might call foul here saying "Hey that's not a surface!" and you'd be right. But ITS has an answer for that too. You can project a feature line to the original work canvas or you can create a new grid based on any surface by using the Create Working Element from Surface command.
The command is simple, launch it, pick a grading grid, then pick the surface.
Now you have a grading grid that can be used to drape a feature line.
Now for the "kind of" part. As far as I can tell, a grading grid created from a surface is not dynamically linked to that surface. I can't even find a way to update the grading grid after the surface is changed, other than creating a new grading grid. So there is no dynamic relationship between the feature line and the surface...bummer. Maybe this is something that Autodesk can add in the future?? UPDATE - Be sure to read Smita's comment below about this very issue.