The present research relates to the field of satellite deorbiting. In particular to research in space structures which facilitate deorbiting of satellites from Low Earth Orbit (LEO). A deorbiting subsystem for spacecraft in LEO is presented, i.e. a so called Self-Deployable Deorbiting Space Structure (SDSS). When deployed, the SDSS increases the drag of the spacecraft by a factor 10-100, thereby slowing down the spacecraft, so deorbit is assured. A method is devised to pack/fold, stack/pack and unpack/unfold a Deorbiting Space Structure (SDSS) supported by a flexible frame so that gravitational issues are avoided, a correct unpacking/unfolding is assured, and the energy supply/propulsion for the unpacking/unfolding process is minimized.