Most electric kilns are UL Approved. Kilns will not cause a building fire if properly installed. The floor under the kiln should be something like concrete, masonry, or brick. Kilns come with instructions about wall clearance requirements that need to be followed. As it overheats, the kiln elements eventually burn out. When the elements burn out the electrical circuit is broken and the kiln begins to cool down.
Nothing flammable should be placed or stored, even temporarily, in the kiln area. I have seen frightening situations where art teachers had thoughtlessly stored combustible materials too casually and too close to the kiln area.
Of course the artwork, if made from low fire clay, will melt and possibly damage some of the kiln bricks. If the artwork is made from high fire clay, the clay may still deform and glazes will likely still run off if the kiln fires too long.
HOW TO IMPROVE EDUCATION
When presenting a rationale about an art facilities and equipment, I generally point out that our choices need to be based on what is best for the education of our students. We do not build a gym for the coach. We provide safe facilities and equipment because of the benefits to the students. Teachers, administrators, school maintenance workers, custodians, and outside contractors like insurance companies sometimes need to be reminded about the mission of a school.
The health and safety of the children and workers is the first concern. Education is second. Preservation of property is very important, but would probably be third on the list. If we select an insurance company that puts too many limits the education of our children, it may be time to get three bids on insurance--not merely based on cost, but based on cost AND benefits.
If a kiln is safely installed and nothing combustible is nearby, it seems safe to fire during the night if somebody checks it the morning after. Night firing is commonly done to avoid breathing the fumes when the vent system is not quite adequate.
If finishing the firing after work is not allowed, it may be possible to set the kiln on a low or slow setting overnight during to pre-heat it so the firing can be rapidly finished during the school day.
If this is not possible, it may work to use a two day cycle. Use the first day to pre-fire the kiln a low setting to dry out the artwork thoroughly. Turn it off for night. On the second day, do a fast firing so it finishes off during the school day.
FAIL-SAFE BACKUP ALTERNATIVES
If an insurance company proposes a costly fail-safe operation that takes control away from the teacher, perhaps they would also be willing to look at alternatives that are less costly to install. It may not cost as much to install a heat sensor that would cut the power to the kiln if the room temperature gets above a preset point. A single sprinkler head installation in the kiln area may also be a less costly alternative to taking the control away from the teacher.