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I have a basic sphere, and with Freehand Addon I have created an arc and bevel that with the circle. To the arc its been bevel like a tube shape.
Tube shape 
Adding Shrinkwrap modifier the tube shape became flat
Tube flat 
Why has the tube gone flat after adding shrinkwrap modifier?
There is a button Apply Modifier on Splines' Points that you have to enable.
With the function deactivated the curve will get beveled and the resulting surface will receive the shrinkwrap modification. With the function activated all of the curve's control points will be shrinkwrapped. The bevel will then be applied to the shrinkwrapped curve.
