With all real respect for the concerns and aitzas expressed above, I think the main thing that has to be checked is CHILDREN.
I think that if we (could) know what started a very large percentage of Shabbas/YomTov fires, we would find that unattended children are often responsible.
By unattended children I mean such things as (but not limited to…) kids running around during the Shabbas night meal (while the adults are shmussen at the table) and knocking into the still burning candles, or banging into, or putting flammable materials near or under the blech in the kitchen.
Also kids may get up earlier on Shabbas morning than parents, and go to the kitchen for food or to play BY THEMSELVES!
Parents MUST be more diligent in watching their kids to prevent tragedy, EVEN IF it means interrupting your adult table conversations, and/or getting up earlier in the morning.
Most homes in New York are built largely of wood (even if covered with brick) and sheetrock, and can, chalila, go up in flames really quickly.
Another very important issue…
Make sure to have WORKING smoke-detectors on every level of the house, AND a working fire-extinguisher on every level of the house.
If you don’t have your home equipped already with these items, get them NOW, BEFORE NEXT SHABBAS.