Atop the points mentioned by ThePiachu, 3rd Edition gave us the Exigents, which are empowered by a god. This Process takes a shard of the God's essence and might burn out lesser gods when they have to take a larger part of themseves. This way several gods (like the one empowering the 'iconic' Exigent of the harvest) do cease to be. While this way to create an Exaltation is not really an option for a god without an office and purpose (unless it still has retained some aspects of their former office), there is also mentioned, that there would be something like a "black market" for Exaltations in which an exaltation can be seriously altered.
Now, why do I bring this up? It is because of the very later part: A God fallen to unemployment might come under pressure and become a criminal god dabbling in the black market. While that does not give him office and stipend, he might have contacts and influence still, kind of becoming a mobster and funding his life in Yu-Shan with that income. On the other hand, he might try to get in control of an Exigent-Exaltation and use it on some mortal in order to gain followers and cult on earth, giving him prayers and thus a domain again.
While this information surely might be useful to work out an individual unemployed god, it does hardly give any solid information.