It is not common for animals to die in the chimney, but it does occur, especially with those slick metallic chimney flues. When it is a hay flu, then the critters are always able to crawl out. However, baby raccoons and squirrels are extremely common in chimneys, and infants have a higher mortality rate. Or they might crawl through an open damper, then the mother does not come down to the fireplace for them, and they expire in the fireplace area, sometimes behind a panel, if there's one. These cases are typically not too tough, but when a squirrel expires between two metal tube flues, then it is game over. There is no way to get that area. You just have to wait for the creature to decompose and become a mummy, and the odor will go away. Place a fan in the fireplace and then point it up. This is pretty much the only case where it is impossible to have a dead animal removed, but those steel chimney flus are infrequent, and more prevalent in the south.
I get a whole lot of calls about dead animals within the ducts, vents, or AC system of a home. I've seen it occur about ten times. However, it's a lot more common for the creature to die under the home, or in the walls or attic. The odor molecules congregate in one place, then when the homeowner turns on the air conditioning or heat, the air gets circulated along with the stench and gets swirled around and you suddenly get a big whiff of it, and you assume that the creature is in the heating/cooling system ducts. But that's not generally the case.
If the dead animal is at the wall, then I have got to cut it out, plain and simple. In rare situations, I'm ready to go up in the attic and look down the wall and use a particular trap tool or grasping tool to find the dead creature, but the majority of the time that I've got to cut a hole.So as to find the specific spot where I want to cut a hole in the wall, I must sniff and sniff. If I have narrowed down the area, and the creature isn't in the attic or under the house and certainly within the wall cavity, I stick my nose right on the wall and sniff every square inch till I hit the specific spot. Believe me, when I reach this spot, I know it. The smell isn't only more powerful, but it changes in character. The wall is even occasionally slightly warm as a result of slow combustion process of decomposition. When I find that area, I cut a hole open and remove the creature.
Occasionally a creature just falls down a wall, and can not get out. I've seen this occur with mice, rats, squirrels, opossums, and raccoons. The walls of drywall are extremely smooth, and difficult to climb. If you hear scratching in the base of a wall, then you'd better do something about it, or the animal will suffer and die, and then lead to an odor you don't want.