The shrinking of the United Federation of Planets from about 350 member worlds to 38 in the century after the Burn, as warp travel failed and worlds such as Earth and Ni'Var withdrew.
The collapse of the Federation is the situation Michael Burnham finds in the third season of Discovery. Around 3069 the Burn made most dilithium explode in a single moment, destroying every ship with an active warp core. Long-range travel and communication broke down, and nobody knew the cause.
In That Hope Is You the lone officer Aditya Sahil has kept watch at a relay station for decades without hearing from his superiors. Earth has turned inward and guards itself against raiders, as seen in People of Earth, Ni'Var has left, and Starfleet Headquarters lies hidden behind a distortion field under Admiral Charles Vance. The Emerald Chain, an Orion and Andorian syndicate, has taken over much of the old territory.
Recovery starts in 3189 when the Discovery crew trace the Burn to its source and reach a new supply of dilithium. Under President Laira Rillak old members begin to come back.