This is most probably mold...very common in older AC units and can even occur in newer units that got moist (from normal use) then were shut off for a while. It happened to mine from gust being shutdown for a few days in the humidity.
Of-course mold is not healthy and can cause an allergic reaction in you and possibly your kitty and it is causing the unpleasant odor...but it should be very easy to take care of yourself. BE SURE TO TURN OFF & UNPLUG THE UNIT!!!!
Mix 1/2 cup of chlorine bleach with a 1/2 gallon of water, pour into a clean squirt bottle, take out the filter and thouroghly squirt the 'fins' of the AC unit from the inside of the house. Wash down with a water soaked brush and/or cloth and be sure to get as much bleach water as you can up into the bottom of the unit from the inside. Don't worry about trying to clean it out of there as you will do that from outside.
Then go out side and drench all the 'fins' (coils) of the unit that are exposed and even pour the bleach water solution into openings in the unit. (The 'fins' or coils I am refering to are the parts of the unit that look like the main part of a car's radiator.)
Anyhow, after you've totally drenched the unit with bleach water...get out your graden hose and rinse everything you can with high pressure water. Rinse/rinse/rinse/rinse. You'll be surprised at what all gunk comes out of there. Scrub the'fins' if needed.
Let it drain for a bit (20 minutes of so)...
Wash your filter in bleach water if you can... (but if you can't - well AC's can run without filters...you just have to clean the fins every other day or so)
And wipe it down inside and out, then restart. The foul odor should disappear soon if not immediately and the bleach will kill the mold. This is considered AC maintenence and is the first thing a repair person would do.
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