move pivot to the side you want stuck on the edge of path (ok experiment first you probably wont get this working on first try).
then atach the object to path via path animation. set the up vector so that the object is like you intended it to be on the path.
open the path animation in the atribte editor and disconnect the anim curve from the position (so it will stay still)
flow path, with latice along curve option! make sure you have steps enough (dont worryy ou can edit this later).
scale in the direction along path wit will now deform just remeber you need eneough detail to make it deform good!
problems:
flips arlong curve! reason normal not clearly defined in local up direction on a normal curve. solution: use curve on surface
problem deforms badly. two reasons 1 not enough deformable detail. Solution increse detail. Problem 2: original bounding box not big enough redo from step 1 wit max intended scale! (note sale along path is irrelevant for scaling purposes as long as the object is shorter that the path)
Also as allways any history ittem can be animated for slithering effects etc etc.
not perfect but pretty damn close!
