Do Elizabeth Midford and Ciel Phantomhive stay together even after Ciel turns into a demon in Season 2 episode 12?
At the end of that episode, it was shown that Ciel went to leave his mansion along with Sebastian. Sebastian then jumped off a cliff with Ciel on his arms. Considering this, it is very likely that Ciel didn't stay together with Elizabeth. He left her (dumped her, whatever you call that) to go with Sebastian, possibly to the underworld, considering the settings of the manga and anime.
He never had a genuine emotional connection with her and they were never together in the first place, so it's not like he loves her and wants to stay by her side. He cared about her but it's clear he never intended to marry her, particularly as he knew he would die sooner than that. After getting turned into a demon, he decides to start an entirely new life. He gives Lizzy the last dance as a gift and that's it. Ciel never had romantic feelings for her, so I can't see why he would decide to return from hell, where he and Sebastian headed, to reunite with her. It'll be easier for her, too: they were always incompatible but now Ciel can't even die, so she'd be unable to have a normal life with him anyway.