How to make the correct shape using the curve modifier?

I cannot build a form so that the object does not unfold on the other side. Maybe there is some other way to do it.

I want to make a piece of skin that goes around the oval object to the bottom

This is what I get

I don’t understand the question exactly… :thinking:
If you want to change the direction of a wide area, select Vertex on the curve and rotate Ctrl+T.

You can check the manual for more information.

You might have a look at the curve controll point tilt angles: