The part in the example image isn't sprung - its fixed to the inside of the tail gate.
The sprung part is called a "Loading Sill Cover" - BMW# 51478402127 - Part #11 in this diagram...
RealOEM.com - Online BMW Parts Catalog
It may be hard to repair the springs if they are broken...
https://www.ecstuning.com/b-genuine-...z/51478402127/