ECUSA is not, by any means, the only institution of Anglicanism in this country. There are more than two dozen church groups that follow Anglican liturgy and tradition operating around the nation. The Reformed Episcopal Church has been around for over a hundred years.
Technically, ECUSA is the only American branch of the Anglcan Communion. The Network, which is headed by Bp Duncan, is part of ECUSA. However, a number of other branches (such as Nigeria, Uganda, Bolivia and SE Asia) have either launched parishes or given oversight to existing parishes that are geographically located in the United States. These parishes and their clergy are members of the Anglican Communion because they are part of an overseas Anglican province. The most well known of these groups is the Anglican Mission in America (AMiA). Its bishops are part of either the Anglican Church of Rwanda or the Anglican Church of SE Asia. There is widespread speculation that the Anglican Communion will expel ECUSA, and the groups in the US and Canada that are overseen by foreign archbishops will be rolled together into a new North American jurisdiction.
In general, ECUSA parish property is owned by the diocese. However, the diocese also is ultimately responsible for the parish's liabilities. From a diocesan standpoint, a parish walkout means the diocese looses that parish's annual contribution to the budget and inherits the mortgage, maintenance, utility and insurance bills. Having several parishes leave could force the diocese to the bargaining table (sell to the departing parish the property) or into bankruptcy court.
There is little ECUSA can do to AMiA churches other than complain to Archbishop Williams about foreign bishops "invading" ECUSA territory.
That is what the Bishops would like for you to believe, but in most instances that is not the case. Most of the established parishes hold legal title to their property. Recent rulings in Calfornia dealing with Methodists and Presbyterians have held that legal title, absent an express trust of record, controls. So in California, at least, the local parish might well be able to hold their property. Outside California, you would need to research state law, which might still not be conclusive on the subject.
If the court is willing to use neutral principles of law, the parish is more likely to win; if the court defers to the religious body, the bishop is going to win.
Some of the parishes have elected to walk away from the property, even if there is a good likelihood of success, because they don't feel that the legal battle is a good use of resources.