There is a couple of o rings at the bottom of the dip stick tube. The tube is bolted to the cylinder head, which is why I find it strange that it would pop out of the block. My thought is that it happens during service like tranny work or head work. I know one of the ones that I've had that had the tube out had a new tranny in it, but I can't say for sure about the others.
The dip stick tube it's self will not make a burning oil smell, BUT the oil will blow out of the hole and drip on to the a/c compressor heat shield and then drip on to the exhaust. The oil on the exhaust is what makes the smell AND posses the posibility of an engine fire.