If an OSPF leaf area becomes dis-contiguous can hosts in one half still communicate with hosts in the other half? Both halves are still connected to area 0.
without any route summarization at ABRs there is no problem if a non-zero area is partitioned until both halves are still connected to the backbone area.
if area range commands are defined on both ABRs the risk is that from the backbone area point of view there are still two exit points for the summary route(s).
LSA type 3 are regenerated at areaa boundary and they don't have an original area-id.
So without summarization routes can be exchanged via area 0.
So ABR1 of semi-area A1 will accept LSAs generated by ABR2 of semi-area A2 and viceversa.
Between areas OSPF uses a distance vector approach.
Hope to help