This is a very interesting thread.
My cat has a bad habit of peeing on the floor next to the litter box instead of in it, about every other time. She has done this since she was a kitten and no amount of switching types of litter or types of litter boxes has ever helped. As such, her litter box is in the basement in an area under the stairs where it's just bare concrete under the box instead of upstairs where her messes would be a problem. I've been regularly pouring full strength bleach on the concrete floor where she has peed in order to get rid of the smell for the past couple of years. I figured that it worked so well because the bleach was reacting with the ammonia and chemically neutralizing it (I do this only once a day, so the urine has had ample time to degrade into ammonia). As another poster mentioned, the area fizzes and heat is released in addition to what smells like chlorine gas. I have to leave the area for a little while if a large quantity of urine was deposited on the floor due to the chlorine gas, but after an hour or two it dissipates (I'm assuming that the CL gas is quickly reacting with the surrounding air and being converted into something less reactive, which is why the smell only lasts an hour or two, even in a closed house). The cat is smart enough not to step in the area on the floor that's been treated, and apparently after it dries nothing harmful is left, as she has walked on dried areas without apparent effect. Also, as someone else noted it looks like some white crystalline precipitate is left after the reaction is finished and the water evaporates. Every couple of months I completely clean out the area with some other cleaner that doesn't contain ammonia in order to remove the precipitate.
I'm curious as to what the gas is if it's not chlorine (someone in this thread thought that the gas was something else), and I'm wondering what the precipitate is (could it be salt?). If someone here works in a university and has access to a lab I'd be happy to send them a sample of the precipitate for analysis. That might help answer the question about whether anything dangerous is being left behind after the reaction is complete.