That's typically not what happens - you either get bloody revolution or people just ignore the rules that aren't giving them a fair shot ( ie turn to crime - ie state disapproved activities ).
This is what has traditionally held back the elite from their worse excesses - they don't want to live in a world where either of those things happen.
ie what's the point of being rich if you are constantly worried about yourself or a member of your family is going to be violently kidnapped etc.
As to your first point - it's a bit like the first - if there is no social safety net, then it you could happen to you - you could get ill, lose your job etc. Even if you believe the system is created by total self-interest - then the past has shown that the equilibrium involves looking after everyone to some extent as:
1. It could be you one day.
2. Having lots of desperate people, even if it isn't you, is in no-ones self interest.