Like the title says, Prussia survives. Albeit, a lot smaller (maybe current day Kalingrad with parts of North-East Poland and Eastern Lithuania, basically the Duchy of Prussia borders).
As for what causes this: Wilhelm II somehow escapes to Prussia and establishes his small kingdom there (along with those loyal to him). What happens with WWII (assuming the rest of German history is relatively similar, with Hitler and the Nazi's still gaining power), who do they ally with and what is the small Kingdom's future for the rest of the 20th and into the 21st century (what's their relations like with Eastern and Western Germany, how do they deal with the USSR as well as the rest of europe post WWII.
As for what causes this: Wilhelm II somehow escapes to Prussia and establishes his small kingdom there (along with those loyal to him). What happens with WWII (assuming the rest of German history is relatively similar, with Hitler and the Nazi's still gaining power), who do they ally with and what is the small Kingdom's future for the rest of the 20th and into the 21st century (what's their relations like with Eastern and Western Germany, how do they deal with the USSR as well as the rest of europe post WWII.