This can be resolved with a process called decoherence. A large(macroscopical) object isn’t exactly like an atom. It is made up by some times millions of atoms. And it’s a averaging out of all these wave functions which creates the large object which we sees . Now, I said that the device and the cat were in a completely sealed container, but that was in parts a lie, it’s extremely hard to get a object completely isolated there will always be for example atoms in the air that collides with the object, or maybe a lamp in the container sending out photons. All these interactions constitutes measurements of the atoms in the object. Which means that their(the atoms) wave functions are constantly changing. And all theses changing wave functions have a very little chance of together creating a half-dead half-live cat state, which there’s only one of. Instead it will probably collapse into either one of many a certain dead or certain live states. Therefore the device measuring spin can only be classically up or down, the cat can only be shot or not shot, and only dead or alive. They do have a probability of being in both up and down and both dead and alive super positions. But these super positions are incredibly rare and if they would appear, they would disappear at once due to the changeing wave functions. Note, that even though the wave functions are still changing, a spin measurement device which comes out up on a measurement wont suddenly change and show a down state, very much like a normal particle which has been measured to have spin up wont change into spin down. the measurement device will however change between all the possible showing-up states there is and so will an alive cat keep change between all the possible alive cat states(because of the constant interactions). But the uncertain dead-and-alive state, being in the middle, can change into either dead or alive state and will do so pretty quickly but when it finally has changed into either dead or alive it will stay there. So that’s why we wont likely see a half dead-half alive cat.
Another strange thing is that, in a dead cat, the alive states will continue to evolve separately from the dead states, even though we only see the dead states. So even if we only see one state, all the separate states will continue to exist and evolve not caring about each other. So it’s not only a averaging of the wave functions of the atoms in an object, but also a averaging from macroscopically waves functions of the object.
And this is quite interesting. You might have thought that when you measure a particles spin and it comes out up, the down state doesn’t exist at least not anymore. But on a closer look this would violate Bells theorem, there are no definite states.
You can see this in a example:
Suppose you(please don’t involve me) measure a particles spin on a verticle axis, the spin can now come out either up or down lets say it comes out down. Then you measure the particles spin 90o from that, on a horizontal plan and it can come out either right or left, it comes out right. Then if you turned the measureing device back and measured the particles spin on a vertical axis again, would it come out down again since that’s after all what we measured it to be the first time? But then you would know both its spin on one axis and its spin 90o to that axis, and this actually violates the uncertainty principal. So when we again measure it vertically the chances are still 50/50 that it will come out up or down. So one particle state doesn’t disappear because you measure it to be in another state. And this is what makes both dead and alive cats exist at ones. The particles making up the cat have properties, and as we have seen these properties exist independently of each other. And as the cats properties are determined by what properties the particle which makes it up has, if you just changed one particles state you would have a different cat, so there also exist different cats parallel to each other, since the particles making up the cat have properties parallell to eachother(further down on this doubtful QM intro you’ll find something called many-universe interpretation. Note that what we discuss now has nothing to do with it). There will exist almost an infinite number of possible dead cats and another infinite number of live cats, and of course one half dead-half alive which requires for all the particles to be in a specific state.
However decoherence is a field under development and we can’t be certain that it’s right.