Well, as a first point, OP's information is wrong. While it's true that the half-life of U235 is ~700 million years, it isn't true that half of the initial mass is lost. When U235 fissions, about 200 MeV of the initial mass is converted to energy. The total initial mass is about a thousand times that, though (E=mc^2). So, after 700 million years, assuming you kept it from falling apart, the initial 15 lb lump would only lose ~1/4 of an ounce as energy.

For the case of U-235, which undergoes alpha decay, when an atom radioactively decays 2 protons and 2 neutron, essentially a Helium atom, are ejected from the nucleus. What remains is Th-231. So if you have 10 lbs of U-235 and wait out it's half life, what you would have left is 5 lbs of U-235 and 4.915 lbs of Th-231 all mixed up and the remaining 0.085 lbs off somewhere as the He particles.

It turns into funny juice (the subatomic particles or photons are flung out to go do stuff I'm not smart enough to explain further)

It doesn't get destroyed, it just splits into smaller things. Decay chains contain a number of reactions, which involve emission of a particular "particle": alpha particle (helium nucleus), beta- particle (electron), beta+ particle (positron) or gamma particle (photon), accompanied by stuff like neutrinos and antineutrinos. Thus a radioactive sample "loses" mass and energy. You can also have nuclear fission, where a heavy nucleus splits into smaller nuclei.

This isn't the full scope of nuclear reactions (there's stuff like electron capture, proton/neutron emission, etc.), but it should explain the problem at hand.

Edit: obviously half-life doesn't mean after that time sample shrinks in half, it means half of the original isotope remains while half has decayed. There would be lead and unstable decay products in the sample still. Radioactive isotopes don't decay to nothing, they decay to stable isotopes.

If it’s a principle rule of the universe that matter cannot be created or destroyed

That's where you're wrong kiddo.

You're only half right there. The conservation is not of just matter, energy must also be taken into account.

Matter is not destroyed, during radioactive decay some of the "matter" is released as energy in form of radiation.
I'd like to also point out that nuclear decay doesn't "evaporate" matter. It's reduced to stable state, which might be different isotope of the same element, or element with lower amount of electrons.
Another point that I'd like to point out is that I'm not a physicist, and this is oversimplification, and probably wrong at some points, but that's my rough understanding. I am absolutely sure though, that you'll not get half mass of whatever you had before after one half life cycle.

One crazy-ass thing about atomic nuclei is that they actually have less mass than the sum of their parts. The more stable the atomic nucleus, the more mass is "missing" relative to the isolated baryons.

https://www.nuclear-power.com/nuclear-power/nuclear-energy/mass-defect/

So as nuclei are marching towards the stable ones at the end of their decay chain, they lose mass not simply because alpha and beta decay evolve ejecting particles with rest-mass, but also because more mass disappears into the nuclear binding energy.

I agree it is weird, but it's observable, not theoretical.

In short, it is no longer considered a principle rule of the universe the matter can not be created or destroyed. Rest-mass can convert to energy (indeed, at small scales, it happens all the time, like in the banana on your counter).

What thisbejacob@lemm.ee said.

But I wanted to add that it's not a fundamental rule of the universe that matter not be created or destroyed, only energy.

Antimatter can annihilate matter and release photons, for example.

I imagine it turns into energy

It's not like the matter stops existing, it just stops being that specific element.

In the case of uranium, natural decay is mostly alpha radiation, meaning that 2 neutrons and two protons are ejected as a (high energy) helium nucleus, while the parent atom becomes thorium with an atomic weight four lower (e.g. U-238—>Th-234).

It doesn't just disappear right, it becomes something else. It converts to a more stable isotope. I think.