I would hope that pastoral care would be more important that exclusivity*... I mean, this isn't exactly like guarding the communion chalice, though it is obviously still quite an important thing. When my unbaptized infant brother died, my lapsed Catholic Father sought burial in a Catholic cemetary, and was allowed to do so. That one act probably did more for making him more attentive to God and more responsive to Catholicism than a thousand sermons or arguments or billboards or tv shows could have.
*I am not intending this word to be a pejorative here, I understand the value of exclusivity in some aspects of Church life.
When I was 21, a lifelong friend of mine took her own life at the age of 19. She was Ukrainian Catholic and I was Ukrainian Orthodox. Our families had been friends for 3 generations.
Upon news of her passing, her family told her priest it was an "accidental" overdose of pills so that she could be buried in the Church.
The fact that her family had to lie had me very distraught, so I consulted my priest about how the Orthodox Church would have handled the matter.
He affirmed the need for pastoral care in such a case, and that, as others have said, unless someone was killing themselves out of spite, or to "stick it to God", the Church would normally perform the burial. Even in a case of spite, one has to wonder about the mental state of such an individual.
Suicide is not an option a clear minded, happy person considers. For someone to take their own life, they must be so distraught, or under such emotional agony that I think it would be completely contrary to Christ's teaching to minister to the sick for the Church to deny a burial.
The Church is not in the position of judging people's souls. That is God's job. Some like to say that suicide equals automatic damnation. I've never heard the Orthodox Church teach such a thing. (I could be wrong.)
We don't know how our prayers effect the souls of the departed, but I don't think praying for them can hurt. Furthermore, the healing and ministry it can provide to those left behind is priceless.
As I contemplate Jennifer's death, I am also reminded of a thread we had on this forum here about two years ago, "A Terrible Tragedy
+Metropolitan ALEXIOS, being the good shepherd that he is, allowed Stephanie to have a Church funeral/burial.
I would hope that the same economia would be dispensed to any family in such a situation.
Note: I believe "On the recent tragedy in the Atlanta Metropolis
" also offers some insight on the Church's feelings towards suicide.