Can you get sick from living around something dead?

Okay, so there's been iguanas in our vents and we used to hear this iguana scratching at the ceiling, but a couple of weeks ago it stopped. Now it smells like something has died in our office and we're sure it's coming from the vents. Can we get sick if something isn't done about the dead iguana in the vents? Cause I know they say like dead birds and rodents, etc can make you sick, but I'm not sure why?