At a base level, carburetors meter the amount of fuel they let into the engine by the amount of air that is moving through them.
Vacuum is created by the piston moving in the engine and creating an open space. As the piston moves down, it creates an empty volume which pulls in air through the only opening it can find, which is the passageway through the carburetor. So, for example, a 25 cubic inch cylinder is going to try to pull in 25 cubic inches of air in through the carburetor.
However, if the throttle plate is partially or fully closed, it's not going to be able to get that much air in since there's a restriction (much like trying to take a full breath of air through a straw). The more the restriction, the higher the vacuum.
Generally, the more throttle you give it, the more the throttle plates open, and the more air it can get in, so the less vacuum there is. Designers quickly realized that the higher the engine vacuum, the less fuel should go into the engine (since more vacuum means less throttle is being applied). And visa versa the lower the vacuum, the more fuel should go in. From there, they set up all sorts of metering tools in the carburetor to do that.
So, that being said, when you let off the gas and coast downhill, the throttle plates are fully closed and your engine has a LOT of vacuum, especially at high RPMs. Since that's the case, even though the engine is spinning very fast, there's very little air moving through the carburetor since the plates are closed. In this condition, the carburetor will go into idle mode and release as little fuel into the engine as possible.
The only issue with this is that when you're going downhill in the condition you described, there is a lot more vacuum than there normally would be at idle due to the high RPMs. At idle, a healthy engine creates around 18 to 20hg of vacuum. When you're coasting downhill with the throttle closed, it can get as high as 25hg or more. So, even though the carburetor isn't designed to release a lot of fuel into the air stream, the extreme vacuum can actually pull fuel out of places it's not supposed to normally come from under those conditions, which can make the engine run rich.
Either way, the carburetor doesn't care if your engine dies or loses momentum. It just meters fuel into the air passing through it. That's all it does and nothing more. If you're coasting down a hill at 3000 RPMs, your carburetor only meters fuel into the engine because air is passing through it. The only thing keeping your engine speed or momentum up is the spinning of the tires, the momentum of the vehicle, and gravity.