You can't bend a layer into z space in AE. I'm betting that was done with something like Trapcode 3d Stroke, or in a 3d app.
You can sort of fake it by taking a layer in which a mask grows across a layer, butted up against a duplicated layer sequenced ahead in time and rotated and positioned in z space so that when the stripe reaches the other side of the first layer, it draws again across the z rotated layer.
But it's pretty tough to get the subpixel positioning just perfect so the corners butt up against each other properly. The default camera gives unconvincing results to my eye, but changing the zoom factor may help (or hurt).
[Joey Foreman]"But it's pretty tough to get the subpixel positioning just perfect so the corners butt up against each other properly. The default camera gives unconvincing results to my eye, but changing the zoom factor may help (or hurt)."
The best way to get these 'stripe' elements to meet at a corner is to parent the secondary stripe to the primary stripe, then all of the transform properties of the secondary will be in the primary stripe's local coordinate system.
For example, if you have a 1000x100 solid 3D layer (A), and you rotate it 45° on the Y axis, you could either do some painstaking math to figure out where the next solid layer should begin, or you can create another 1000x100 solid 3D layer (B), parent B to A, set B's anchor point to [0,50] (the middle of the left edge) and B's position to [1000, 50] which is the right edge of layer A.
[1000,50] is not the right edge of layer A in world space, but it is in layer A's local space.
Then you can rotate layer B on the Y axis to produce your corner. If you want it to be a perfect 90° angle then zero out the orientations and set the Y rotation to 90.
For the next (tertiary) segment of stripe, parent it to the secondary stripe element.