This question is misguided. A property is not a concrete thing so it is incorrect to speak of breaking it down. (It means something you can say about a substance or an object.) I suspect you mean what type of substance cannot be broken down any further, and the answer to that is an element. It is a property of an element that it cannot be broken down even by chemical changes.
i think an atom
No
An element is the only substance that cannot be broken down.
Atoms cannot be broken down into simpler substances
an element is a substance that cannot be broken down into a simpler form by chemical means
molecule
An atom is smallest particle there is and it cannot be broken down any more.
A substance that cannot be broken down any further and stays the same substance would be an element
unbreakable
If it is in your blood already then you have the disease. You cannot re-infect yourself with something which is already there.
You cannot preserve something that is already extinct!
Cannot be broken
because it is like a rule of science that cannot be broken. it is impossible to be broken. there are theories which aren't proven yet but laws are proven already
Ghosts CANNOT be killed, you can't kill something that is already dead.
No
You cannot fix it. It is broken and cannot be changed. You must get a new one or something.
Something that cannot be broken down or obtained by electrolysis, so in short, something that is not ionic. For your purposes a good example is probably sugars.
An item that is not biodegradable is something that cannot be easily broken down by living organisms. A usual can is aluminum and this material is not biodegradable.