an asylum seeker can of course buy a house. Why? Because it's, among other things, a human and a fundamental right. For details see German Wikipedia, catchword "Eigentum": http://tinyurl.com/z2e9ukg
(translation by Google translate). Fundamental rights are irrespective of one's financial situation. Asylum law in Germany is based on a fundamental right. So property can't take from my point of view any effect on the asylum procedure.