In Matriarchy subsistence is until today the only way to provide goods for the community and standing for autarchy.

Private ownership is unknown.

Inheritage is matrilineal, that means passing from mother to the (often youngest) daughter.

So, what could be inherited, if there is no private property? 'Things' like:
- Responsibility for well-being of the clan
- Responsibility for distributing goods and work adequate  
- Administration of the clans common property
- Responsibility for keeping the fire alive in the family hearth
- Taking care of the children equally 
and more suchlike lifetime tasks...