Soviet rump state ... maybe some central Asian republics would choose this as a way to stave off further desintegration, fearing wars and chaos. They may want to hold on to what nuclear weapons they have stationed within their borders, at the time when Moscow sought to move all such weapons to Russia before things fell apart.
Suppose they had a few nukes; that would give them some insurance against invasion. They would talk of safeguarding the Soviet ideals, carrying on as the source of truth until a better future arrives. Harkening back to stronger days would give people a sense of security and stability in an era where everything changes. They would want closer ties to any strong states they could find - China, Pakistan, Iran would come to mind. They would still hope to establish trade with the West, exporting natural resources.
"When we change, it is by our own choosing!" says the new Chairman in a speech at the recently built First University of the Southern Soviets. "In this university, we will educate the men and women who will safeguard our ideals. The future will come when there is no need to rely on foreign experts in any field - there is nothing foreigners can do that we cannot do ourselves!
"We will not let foreigners decide the fate of the Southern Soviets. Comrades, these are trying times, but we will prevail stronger than ever! We will carry the light to follow for all those of our neighbors who have doubts about the future," the listeners recognize the reference to the Chairman's plan to encourage immigration by wealthier kinsmen from northern states, "and we will stand firm with all our friends.
"Neither decadence nor mysticism will shake our faith. Neither immoral Western values nor religious fanaticism will disturb the path chosen by the Southern Soviets. Comrades, stay true to our socialist ideals! Solidarity means progress!"
The crowd cheers. Finally, a man who knows how to proceed when Moscow has failed to deliver. A man who will beat down the rebels - religious and ethnic - in the countryside until things can get back in order. A man who will allow foreign investments, but keep the media in a firm grip so that the people's minds won't be poisoned.
"Long live the Great Father of the Southern Soviets!" a woman shouts. The crowd takes up the chant.