Always empty your Kenmore dryer's lint tray after each dryer cycle. If lint is permitted to accumulate in the tray for long periods, it's liable to get caught in your dryer's exhaust system and cause a fire. If a lint fire erupts inside your machine, it can produce a strong burning stench that lingers in the drum even when the dryer is off. Since lint fires can harm your dryer, consult a dryer repair technician to evaluate the integrity of the dryer after a lint fire occurs. Thoroughly clean the dryer of lint; removing debris from the trap and entire exhaust system to restore airflow.
If airflow is obstructed from releasing from your dryer, it could also pose a fire danger. When air cannot pass from the drum through the vent to outside, the dryer is prone to overheat. When this happens, it can trip the thermal fuse to stop the dryer to avoid damage. A blown thermal fuse can sometimes produce a burning smell after it has been triggered. Contact a dryer repair technician to inspect the appliance's exhaust system and clear out any blocks. If the thermal fuse has blown, you must replace it; otherwise your dryer's function will be limited.
Ignited Gas Fumes From Nearby Flammables
Keep flammable liquids and solutions, such as cleaners, paints and stains, at least 50 feet from your dryer. The flame on gas dryers is sometimes strong enough to actually ignite gas fumes released from these products. When fumes ignite, they can create a burning smell near the dryer.
You can usually eliminate a burning smell from your Kenmore dryer drum by drying a load of clean, damp towels. The towels help absorb the odor from the air as the dryer heats them dry. Repeat the process until the smell is gone. You will need to rewash the towels once you've gotten rid of the scent from the dryer so it doesn't persist in the towels.