I've covered outhouses and composting toilets, so let's take a look at one final method of dealing with human waste in an emergency before I move on to a less squeamish subject.
Outhouses work well if you have a BOL established, or have a yard to construct one in if you have to bug in. They're a semi-permanent fixture that will serve for years of use and have been around for centuries. Composting toilets are smaller than outhouses, and some models are mobile, but they have more maintenance issues and need to be emptied more often.
For the prepper who lives in an apartment or works in a multi-story building, neither of these options will work if your building is isolated from the normal municipal services. Some scenarios which come to mind:
You're at work on the 40th floor when a crisis hits and you're told to shelter in place. Most situations like this are resolved within a day or two at most, but nobody wants to hold their bladder that long. Street-level riots, flash floods, fires, active-shooter situations, and the like could leave you trapped, and there are multiple reasons that the water could be turned off. I've seen office buildings with key-card locks on every door, including the bathrooms, and a lot of them will stay locked if the power goes out.
Tornado sirens are going off, so you hustle your family into your underground shelter only to have the house settle on top of the shelter door. Emergency services and your neighbors will dig you out once they figure out that you're stuck, but it may take a day to get enough debris shifted that you can get out.
You've taken shelter in a cave with a floor that is too hard to dig into. Unless you find a sizable colony of bats and want to add to their guano pile, you'll need some way to carry your wastes out.
You waited too long to evacuate ahead of the hurricane and got stuck in the inevitable traffic jam for most of a day. The nearest rest area is 10 miles behind you and your wife has to pee “RIGHT NOW!” and isn't going to squat next to the car in view of all of the other unlucky people stuck on the highway.
There is a solution to all of these situations, and it's called a WAG Bag. WAG stands for Waste Alleviation and Gelling, which should tell you a bit about how they work.
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WAG Bags come in a few different styles, the most common being a double-walled plastic bag containing a powder (usually referred to as “Poo Powder”). The powder may be scented, but all variations are hydrophilic (water-loving) gelling agents that will bind with water to rapidly form a gelatin-like mass. The gelling action turns liquid wastes into a form that is easier to transport (it won't spill) and will seal solid wastes to eliminate odors. Most of the bags are made of biodegradable plastic, so once it's full you can just toss it into any trash can and it will decompose in the landfill.
The plastic bags vary by brand; some of them are designed to fit into a bucket or waste-paper can, while others have wide flaps on the opening so you can just hold it open while you squat over it. Watch what you're buying, since the liners for the portable toilets usually don't come with the Poo Powder because they're just a plastic bag system for holding wastes.
Campers who use portable toilets often add clumping kitty litter to the bag after each use to get results similar to Poo Powder, so if you have a litter box for your cat you should be able to make a fair imitation WAG Bag out of two trash can liners and some clumping litter.
If you ever get a chance to explore some of the more remote areas of the world, you're going to find that most of them have a strict “pack out what you pack in” policy. Keeping wilderness areas clean of trash and wastes is important for aesthetic reasons, but the health reasons are more important. Think of all of the people who have attempted to climb Mt. Everest and the waste they've left along the trails: since there are at least 200 dead climbers interred on Mt. Everest, there has to be tons of waste as well. WAG Bags are now mandatory at a lot of hiking/climbing sites, so they're becoming more readily available and cheaper.
A container of Poo Powder is small and fairly cheap. If I were working or living in a high-rise building, I think there would be a few of them in a drawer or on a shelf, just in case. The powder is shelf-stable and has an indefinite shelf-life, so it will store for years.