That is a very good question. Even in a non-cultic situation, the demise or departure of a charismatic leader is a vulnerable point.
Just talk to anyone who has had long experience serving on search committees for Anglican and Protestant churchers, and for Jewish congregations--all traditions in which the community can choose its leader.
Then talk to people who have experience in business and ask them what its like when a charismatic, successful and brilliant leader retires.
It is painful and difficult to be the successor of someone who, literally has been 'a hard act to follow.' Some groups do not make it.
But there are groups that do manage to survive a charismatic leader. If that leader has had an abusive track record several things probably happen
* [b:8fe3563871]Accumulate Assets[/b:8fe3563871]
It helps if a group has accumulated subtantial assets. That means they can afford to publish revised, re-written versions of their doctrine and history
* [b:8fe3563871]Re-write History[/b:8fe3563871]
If possible, re-write group doctrine or history. It helps to have the money to publish new updates. In some cases, a group went to considerable lengths to destroy old documents, even pictures. In the case of Siddha/SYDA yoga, this is described in the New Yorker article, [i:8fe3563871]Oh Guru, Guru[/i:8fe3563871]. [
www.culteducation.com]
* [b:8fe3563871]Blame the Underlings, Excuse the Guru[/b:8fe3563871]
Assure people that the previous bad behavior of the group did not originate from the guru, but from a corrupt inner circle of disciples who decieved the guru. (Note any member of an abusive guru's entourage ought to know that if anything goes wrong, its the inner circle members who often get scapegoated, socially and sometimes, legally, while the guru escapes. All too often entourage members carry the shadow of the group, and the guru carrys only the positive projections of the group--even when it is the guru who is ultimately puppet-mastering the entire thing.
[b:8fe3563871]Offer a New Menu of Services according to Social Needs[/b:8fe3563871]
Re-emerge by offering services valued by society, such as meditation, yoga (especially yoga. You can sell accessories too), and especially schooling for young children, troubled children. I predict that in a few years, offering elder care will be a gigantic growth industry-and it will attract cults. It'll be perfect. Exhausted guilt ridden middle aged people looking for help with aging parents, and aging people who can be conned into disinheriting their kids. Just watch and see how soon cults line up for this one.
* [b:8fe3563871]Change names[/b:8fe3563871]
If a charismatic leader has ended in disgrace and his or her name has become infamous (eg Rajneesh and his Rolls Royces and sexual excesses) ...change the name of the leader. It is astonishing how many new converts do not bother to fact check. Other's who have changed their names have been Da Free John (now known as Adi Da Samiraj).
The old Erhard Seminars Training (EST, known in its heyday as 'no-pee-therapy' because participants were given infrequent bathroom breaks) was renamed The Forum and now, currently, goes by the name Landmark Education.
Finally, make it seem that anyone who has a sense of history and keeps track of this stuff is a negative minded, loveless cynic.
Historians and fact checkers play an essential role keeping groups and societies honest. And they are the ones who catch heat when a group decides to become oppressive, authoritarian, and lie about its past.
One distinguished historian was murdered by the Bolsheviks because he was a member of the Romanov dynasty. Lenin received a plea for clemency and refused it, saying 'The Revolution does not need historians.'