"Built enough" may sound like the same thing as "giving out housing for almost free", but it isn't. Also, cheap temporary emergency housing for a sudden extra burst of refugees may be inappropriate for permanent occupancy, I believe this is an example, it's certainly containerised/temporary *something*: https://maps.app.goo.gl/HUyQS6Sc1w1Y8GUH6?g_st=ic
That said, an idea has come to mind: UK and Italy have had schemes where a home can be purchased for £1/€1 under the condition the new owner repairs them (the repairs would cost 20-150k). Given some of the really bad stock I've seen in some searches, this may be a good idea for Germany too.
No, I'm not stupid or lying.
And yes, it's true. It's just that this housing is not in Berlin.