I think that one of the critical elements in the question is how the lottery is seen as an established part of the social identity. The lottery precludes social breakdown in this setting for a couple of reasons. The first is tradition. There is a traditional element in which the lottery has been a part of the social configuration for some time. It is one in which the lottery has become part of the individual pattern of recognition for some time. As long as there has been a community, there apparently has been a lottery. This was brought out in Old Man Warner's affirmation for the lottery in both age and meaning. Whether it is the belief that crops will yield in better harvest because of the lottery or whether it is that as long as the village has been there, a lottery has been there, the people in the town seem to accept the principle that the lottery should not go away and for this, the society remains intact. Even those who quietly intimate that other towns have eliminated their lotteries are rebuked as "fools" in that the lottery defines the town and the community, at large, seems to accept this.
On another level, Jackson might be suggesting that there is going to be social cohesion when it is predicated upon targeting an outsider. The premise of the lottery is that someone selects the piece of paper to be stoned to death. Jackson might be suggesting that there will be social strength and a lack of breakdown if society is based upon targeting another. When society finds its source of unity in the pain and suffering of others, social orders will remain intact. In the moment when "they were all upon" Tessie, there is no social breakdown evident. Yet, I think that it is important to note that this might not be a good thing. I think that Jackson is arguing that in protecting the rights of individuals, some level of social fragmentation might be a good option. In the end, the social cohesion and lack of a breakdown that is evident is rooted in how individuals target another. When this is present, social orders do not break down. It is for this reason why the lottery prevents the breakdown of society in this community.