If you run the electric water heater without water in the tank, you will burn out the heating element faster than you can read this post.
Actually the hot water heater still holds about 1/2 gallon of water after it is completely drained.
My water heater stopped working off 110v a couple years back. I first made sure the tank was drained. When I unscrewed the 110V heating element, the water kept coming and coming. Many towels were not enough. I called the water tank manufacture to order a new element. The fellow confirmed the tank permanently holds 1/2 gallon of water after it is completely drained, intentionally so to protect the heating element from accidental burn-out. I asked about concern of freezing and he said that was considered in the design of the tank.
If you need to replace your 110v heating element, stuff as many towels as you can under it, and all around on the floor, because once the element comes out, the wave of water comes and comes and comes. I thought I had plenty of absorbsion but underestimated. I ended up blowing a fan in that cabinet for a week to assure all was completely dry.