The community in this book is very controlling and totalitarian. When people break the rules (or at least when they do it often enough) they are "released." This is also done to people when they get too old or when the government thinks there is something wrong with them. Jonas finds out that people who get "released" are given a lethal injection and thrown down a garbage chute.
As far as who runs the government,we don't know very much about this. We do know that there is a Council of Elders that runs things, but we don't know much about them.
Lois Lowry's The Giver centers on a tightly controlled "Community" in which all aspects of people's lives are closely monitored by a group of government officials euphemistically referred to as the Council of Elders and headed by a "Chief Elder." People within the Community are not allowed to experience true human feelings (sexual attraction, love, hatred, anger, etc.), may not choose their own spouses, and are assigned children and jobs. They are emotionally regulated through pills and medications that suppress their desires.
Breaking the rules within the Community can lead to drastic consequences; those who are a threat to the well-being of others (mentally, physically, or emotionally) are "released" to "Elsewhere." Again, this is simply a euphemism for killing, with the alleged offenders being given a lethal injection and their bodies disposed of.