What role can softliners play in a dictatorship?
Hardliners are the people in any government or regime who support strict, inflexible, orthodox adherence to the prevailing ideological system. They are, in other words, the "true believers." The softliners, on the other hand, are the regime-supporters who are more flexible and pragmatic.
The great advantage of dictatorship is that because one person is making all the decisions, it is easy to get things done—as long as the dictator wants them done. The downside of a dictatorship is that one person (the dictator) is unlikely to see all sides of a situation. A dictatorship can easily become so rigid and so blind to the needs of certain groups that this can undermine the stability of the regime.
Softliners can run interference, mediating the gulf between the dictator and his inside cohort and other, more marginalized groups, and, therefore, they are able to help moderate the harshest edges of the regime. They are a group trusted enough by the regime to have some influence, yet they are not blindly ideological: they can breathe some air into a system that might not be able to make the changes needed to survive otherwise.
Within a functioning dictatorship, softliners can play a role by helping to moderate the dictatorship and by making it more palatable to the people who live in it. When there is a hardline and a softline faction under the dictator, the softliners can push for more lenient policies and can, thereby, make the dictatorship not seem so bad. If, by contrast, there are no softliners, the dictatorship will be harsher and may be more susceptible to being overthrown by dissatisfied citizens.
Softliners are also a major part of possible transitions from dictatorship to democracy. During the dictatorship, they can push for more liberalization. If, then, something happens and the dictatorship starts to fall, they can provide a "soft landing." Since they have already lightened the dictatorship, and because they are somewhat trusted by the people, they can serve as a step between the dictatorship and a truly democratic system that might eventually evolve.