From a legal perspective, this is a simple transaction.  The founder and current director select a new group of directors to carry on the mission and then resign to enjoy their new retirement.  There is no “dissolution,” no change of name or exempt status, no outward change that would necessarily affect the other stakeholders in the organization. 

The psychological issue for the founder and the other director is whether they are willing to let go of “their” organization.  Do they need to stay around as “emeritus” directors, with their names on the letterhead and perhaps even status as continuing directors or advisory board members?  Do they leave totally when they get their proverbial gold watches?  Do they continue to help with fundraising?  Do they have different psychological needs that the new board has to satisfy differently?

There are no absolutely right or wrong answers to these questions.  But understanding the needs and desires of those leaving the organization can help make the transition more likely to be successful.