Side note: This could be thought of a philosophy of mind question but as it reads, it seems more like an ethology question, or (animal) psychology question which may or may not be fit for CogSci. That is, it seems you are asking for scientific evidence/research that indicates animals display the same kind of behaviors humans do which indicate an understanding of death. As a philosophy question, it is even more challenging than doing a few research experiments, specifically because it's unclear what it means "to have an understanding of something", let alone an understanding that we are going to die one day.
E.G., Does knowing that when you (or a cat) touch an electric fence that you will get shocked equate with an "understanding of electric fences"? Sure, you understand that fencey = shocky, but nothing about electricity, thermal conduction, grounding, etc. But let's say you believe that such a basic understanding counts as "understanding electric fences". Does it then seem to you that a cat seeing many other cats grow up and die would then understand the concept of death? Does this cat really know that the cat's heart ceased pumping blood to its body for one reason or another? That these final moments of other cats' lives is not just a super long sleep from which it cannot be awoken?
You can see very quickly the difficulty here with your question, and the real philosophical problem behind it:
What does it mean to understand something?
Some notes I have on this subject to get you started, which I wrote down in my initial preparations to write a sentient computer program (that would ultimately be able to understand concepts):
In logic, the comprehension of an object is the totality of
intentions, that is, attributes, characters, marks, properties, or
qualities, that the object possesses, or else the totality of
intentions that are pertinent to the context of a given discussion.
This is the correct technical term for the whole collection of
intentions of an object, but it is common in less technical usage to
see 'intention' used for both the composite and the primitive ideas.
To understand something is to have conceptualized it to a given
measure. The use of concepts is necessary to cognitive processes such
as categorization, memory, decision making, learning and inference.
- Concepts as mental representations, where concepts are entities that exist in the brain.
- Concepts as abilities, where concepts are abilities peculiar to cognitive agents.
- Concepts as abstract objects, where objects are the constituents of propositions that mediate between thought, language, and
–Mostly from wikipedia and other internet sources
Personal addendum: As a physicalist, I believe that "what it means to understand something (as a human)" can be so precisely described that it could be quantified (written in a mathematical formula or computer program), but we are not definitively there yet (at any rate, I don't have the answer yet, but maybe someone else does).