Previous owner says he has no idea what it is, and that it wasn't there when he sold the car. I told him I don't care if it was there when he sold me the car, I just want to know what it is. Still claims he has no idea.
Well, it smells terrible, and I have no idea what it could be.
A friend commented that it smelled like transmission fluid. I don't really know what transmission fluid smells like.
Is it time for a new carpet?
Looks very similar to what I managed to do with a cup of Starbucks and the smell was really odd for some reason.
If it is some kind of oil/fluid... Put some simple green in one of these things:
That appears to be the carpet in front of a forward facing child seat. I'm just sayin' 
If the little green (or a rental carpet cleaner with attachment) doesn't do it then pull the carpet and powerwash it - take it to the local DIY car wash if you don't have one.
I just had bloodborne pathogens training this morning so even though the picture is blocked at work I am going to assume it is an infectious bodily fluid.
There is no better carpet cleaner than a big Landa heated pressure washer.
Tear that carpet out and blast the filth through the backside of it with steamy, sanitizing awesomeness.
new carpet in your future real soon...
Luckily for me, the carpet has a 1" thick section of felt behind it! This felt happens to be soaked in the un-named liquid. It has begun to dissolve the coating on the sound deadening. I decided to cut it right out because I don't give a berkeley! 
It also left a nice '20,000 mile oil change' stain on my nitrile gloves.
Mold?
Used, contaminated hydraulic fluid
I would say a combination of coffee and soda that has rotted through the years. I've cleaned a lot of similiar filth from my used cars. One of them required complete removal of the carpet and a heated pressure washer to blast it out.
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