The whole clan, minus the current clan head Shiki Seishi, are deceased. She and her parents were the only remaining clan members, as most died during the Kyuubi attack, and once they died Shiki was the only one left. It was then that she became the unoffical clan head (clan head's must be at least 16 to take up their position) at the tender age of six.
The Seishi clan may not have been the largest clan (actually, they were one of the smallest) out there, but the quality of ninja they produced was legendary and more than made up for the lack in quantity.
Their bloodline, the Hyoketsu Senkai, is what allowed them to be considered a clan in the first place; the Hyoketsu Senkai was what made the already skilled clan members deadly, giving them control over two of the prime elements, water and wind and, in some cases, the sub-element, ice. Their bloodline was gifted to them by the queen of wolves herself, Ookami.
For a clan member to unlock the Hyoketsu Senkai, they must first experience a moment of fierce protective emotions and/or heartbreak.