When my wife took it out of the dryer, it had a burnt sort of smell to it, but we found what appeared to be a partially burnt item of clothing on the surface, threw it away, and assumed the basket’s smell was just lingering from that.
Nope. Must have been something deep in the pile that was smoldering. A few hours later, we were fortunately awakened by a neighbor who saw the basket (which we left on the porch to air out overnight from the smell) on fire. Thank G-d he was awake and nearby, who knows how much it could have spread! We doused the fire in water, put it all out, but the basket, its contents, and the couch it was sitting on are a total loss. But no human beings came to any harm.
Still no idea just which clothing item was the culprit (no doubt ashes by now), otherwise I’d also have advice about what not to put in a clothes dryer.
If you have a basket of laundry that you think smells burnt, empty it and find the precise item producing the smell! It could save your life!