Having ranted about how people use "Both/And" too often and inappropriately, I am now going to play the "Both/And" card myself. ;)
In regards to the question, "What happens to people in Hell?" the traditional answer is that they are in eternal conscious suffering and the non-traditional answer (or at least the one that I care about for this discussion) is that they are annihilated (possibly after suffering some finite period of suffering).
I would like to raise the possibility that the answer is "Both/And". I should here note that I do not (yet) believe that that is the actual answer. Rather, I want to show that "Both/And" is a viable option as (contrary to all appearances) the two positions are not mutually exclusive.