I have a site that enabled Membership Premium 220.127.116.11 without adjusting any settings that caused a White Screen of Death.
The site is part of a multisite install with a mapped domain.
The user doesn't need the plugin, so I have deleted it for now, but it was enabled and not configured and caused a white screen in WP 3.8. I enabled WP_DEBUG and there were no error messages.
I don't know if this is a known issue, but at minimum, the error reporting needs to improve in this plugin.