Names for organized groups of such a type:
An organized group of people created to assist people based on kinship could be called an "Ethnic Benefit Society" - frequently these might have been mens clubs in the past... "Service Societies" etc
See : Benefit Society at Wikipedia
A benefit society, fraternal benefit society or fraternal benefit order is a society, an organization or a voluntary association formed to provide mutual aid, benefit, for instance insurance for relief from sundry difficulties. Such organizations may be formally organized with charters and established customs, or may arise ad hoc to meet unique needs of a particular time and place.
Benefit societies may be organized around a shared ethnic background, religion, occupation, geographical region or other basis. Benefits may include financial security and/or assistance for education, unemployment, birth of a baby, sickness and medical expenses, retirement and funerals. Often benefit societies provide a social or educational framework for members and their families to support each other and contribute to the wider community.
Words for the behavior of a group helping members of their own group ?
If it is a term to describe the behavior of ethnic mutual aid, try the terms discussed in the Wikipedia articles below.
Take care in discussing these group dynamics as any matter of race, religion or generalizing a behavior is always a touchy subject. These are sociology terms, that might belong more appropriately in a context that has invited such examination.
Ethnic Nepotism at the Wikipedia
In sociology, the term ethnic nepotism describes a human tendency for in-group bias or in-group favoritism applied by nepotism for people with the same ethnicity within a multi-ethnic society.
The term was coined in the 1960s in the context of the ethnic (tribal) tensions and rivalry in the then-recently independent states in Sub-Saharan Africa such as Nigeria.2
... it is a long article with many terms and theories referenced with further links
In-group Favortism at the Wikipedia
in-group favoritism, sometimes known as in-group–out-group bias, in-group bias, or intergroup bias, is a pattern of favoring members of one's in-group over out-group members. This can be expressed in evaluation of others, in allocation of resources, and in many other ways.
This interaction has been researched by many psychologists and linked to many theories related to group conflict and prejudice. The phenomenon is primarily viewed from a social psychology standpoint. Studies have shown that in-group favoritism arises as a result of the formation of cultural groups.3 These cultural groups can be divided based off seemingly trivial observable traits, but with time populations grow to associate
... another long article that should be consulted before throwing the term around