You cannot pay for a white label subdomain. You can however license the engine for internal use only (but pricing makes it only make sense for large institutions).
citation: http://meta.stackoverflow.com/questions/16054/is-the-stack-e...
Re:Slashdot redesign is now in beta
by scott_karana on Tuesday October 01, 2013 @08:13PM
(#6479896)
It looks like at one point, they did used to offer whitelabels:
http://meta.stackoverflow.com/questions/83591/how-to-run-a-p...
Sorry I couldn't find a better link on short notice :)
[citation needed]