An idea that came from the video game "
Ostalgie: The Berlin Wall", one that is highly implausible since even Castro wasn't that crazy and willing to ruin his relations with Germany for very little gain, but theoretically COULD work....
After the fall of the Berlin Wall, have the hardliners of the SED government of
East Germany as well as a group of Stasi agents flee/relocate to
Ernst Thälmann Island in Cuba (Which was 'ceremonially' gifted to the DDR by Castro back in 1972), in order to avoid having to stand trial in the now unified Germany for the various human rights abuses committed by the East German government while they were in power. Perhaps in exchange for the exiled officials of the rump 'East Germany' gifting the Cuban government with the various stash funds and Swiss bank accounts that the East German government have overseas.
With the Cuban-DDR declaring the
Two Plus Four Agreement that allowed the reunification of Germany to be 'illegal', and insisting that the 'legitimate' government of the German Democratic Republic still exist on Ernst Thälmann Island, and the now reunified Germany be considered as 'occupied territory'.
... Of course, this rump Caribbean Germany would have a population of, at most under 500 people, have almost zero international recognition outside of other unrecognised states since no one would want to needlessly ruin their relations with the now reunified Germany and later the entire EU, and would be living off handouts from the Cuban government. At most, it will become a tourist attraction and a curiosity... But it is unlikely that it will last over a generation once the hardliner DDR officials, many of them already just a few years away from death in OTL, started dying off.