How do i fit a mesh to a curve to straighten it out?

Take for example the model listed here:

If i’m not mistaken there is way to fit a mesh onto a curve or vice versa, which would allow one to straighten out flat along the X or Y or Z axis.

I know one can rig the mesh and bend it the same way, however rigging the mesh causes tearing and stretching issues, improper vertices assigned to improper bones and the such, and i am not looking forward to tedious clean up work (unless i absolutely have to, or for minor stuff)

If there are any other methods of straightening a mesh out there, please let me know.

Investigate shape keys. It should be possible to do it with a strip of polygons.

i am a bit fresh to shape key manipulation, but i know how to use them, how does this apply to a line of polygons? im not understanding.

Check out the curve modifier