Doctoral Advising: No Available, Appropriate Chairs I work at a regional university in the United States. Several years ago (before I arrived) our department admitted five years of doctoral students (approximately 50 students) as general admits to a distance doctoral program without assigning chairs. 

Now those students are reaching comps and the dissertation. Four faculty left in the last year which is stressing our already over-capacity workloads. 

Many students are interested in topics for which we have no faculty experts. We are going to hire a new faculty cohort in the next five years but there is no guarantee those faculty interests will match our students’. 

Are faculty obligated to work with and graduate students we did not admit? 

Is there a precedent for such a situation?
Even if it's not "distance learning", there is an obvious hazard in admitting doctoral students that do not fit into the capacity of the faculty. It's irresponsible to the point of immorality. Ok, but/and once they're in your program, yes, your program has an ethical and even moral obligation to serve them well.

There is the complication that, if the students are by-accident allowed to toooo freely choose topics, that it is manifestly infeasible to properly advise them. Someone "should have" explained this to them at the outset. In doing a PhD, "distance" or otherwise, one cannot choose a topic first, and somehow insist that the faculty in the immediate vicinity supervise it. (Nor, of course, is it sane to try to do a project independent of an advisor, or significantly outside one's advisor's expertise. It's hard enough to do a PhD project even when one's advisor is an expert on the topic.)