Kenmore Electric Dryer Model 110-C62662101. Dryer won't stop running. Will run all day long until door is open.

Problem with the timer control unit as it is not switching off until reset with the door latch.
it is possible that the dryer control relay or driver is short and giving power continuously.

Perhaps the timer motor is bad or the gears in it are stripped.
Check the timer motor for continuity. No way to tell by the model number you have posted whether this is auto-dry or moisture sensing.
From my notes: Autodry VS electronic sensing: First, wet clothes are electrically conductive. With electronic sensing dryers as the wet clothes tumble, they touch the two metal bars in the drum. (Auto dry dryers utilize a system of cycling the timer motor with the element, and has nothing to do with how wet the clothes are by the way.) There is a capacitor on the control that is trying to build up a charge, but when wet clothes create a short from one bar to the other, this charge is released to the frame of the dryer, therefore discharging the capacitor. As long as the capacitor charge is low, the control knows the clothes are wet. As the clothes become dryer, they short the bars fewer and fewer times. Once the capacitor charge builds to a certain level, the control knows the clothes are mostly dry, and it advances the program to the final timed portion, usually less than 20 minutes, some of which is a cool down portion to reduce wrinkling. If your dryer is shutting off after only 10 minutes, that means the control capacitor is never getting discharged. This can be due to a few different reasons: 1. Sensing bar wire is disconnected or broken; 2. Load is not large enough (remember the bars must be contacted repeatedly); 3. Bars are "coated" by fabric softener build up and need to be cleaned with Windex or 409. 4. Defective control board. 5. Airflow is restricted and moisture can't escape the drum. 6. Corrosion built-up on sensing board connection.(yank out the board and clean the contacts that sometimes is all it takes) Address the airflow condition and load size. Clean the sensor bars and make sure the wires are all connected securely. There is a diagnostic mode you can enter to test the control's ability to sense the bar contact that is illustrated in the tech sheet which is located within the control panel on many models. No sensing bars means you have auto-dry a totally different animal. Typically an orange wire is connected to the high limit on the heater element housing which feeds the timer motor when the element is not in operation. Bad control thermostat or air restrictions are the Autodry type dryer's worst enemy. Special thanks to a.g.