The comments already are giving you some good tips about how to improve what your model recognizes, but I think your question goes above that asking if there's a way to ensure that it will always recognize the cats.
The short answer is "no".
The slightly longer answer is "yes, but cheating".
Regardless, there are a lot of steps you might take to improve the generalization aspect of your model.
A drama: cat classification in three acts
Act I: Cat as texts
Let's start with an example. Say that your model is trained with these inputs, and learns to correctly recognize them as a cat or not a cat:
cat → yes!
Cat → yes!
ferret → no
cat. → yes!
Cat! → yes!
Three MC's and one DJ → no
Your goal is to train your model so that every new variation, even unseen ones, will correctly be identified.
With a good level of generalization, your model will correctly classify new inputs that it has never seen before:
skunk → no
cat? → yes!
dog → no
CAT → yes
With this scenario, let's say the model now finds this:
kat → ?
Is that a "cat" misspelled? Is that short for Katherine? What should the model do?
Act II: But surely this doesn't happen in real life
Leaving the analogy for a bit, will your model that's looking at domestic cats properly accommodate for Savannah Cats, or will it consider them out? (They kind of look like cheetahs.) What about Sphinx cats? (They look like raw chicken to me.) Elf cats? (They look like bats.) This is just an example, but you can probably figure out more.
And the reason behind this problem is that the distinction itself between different classifications (in real life) is not binary, but rather a transition between "yes, that's a textbook cat" and "that's a chair". Your model will output binary decisions (maybe accompanied by a confidence interval, but even with it, you'll make the call into deciding if it's a cat or not).
Setting specific boundaries will help. You can define that your model will only detect domestic cats, maybe no bigger than a certain size, only of certain colors, etc... This is limiting what the model will correctly recognize as a cat when we (humans) might disagree. For instance, I would still argue that flourescent cats are still cats.
Going back to the simple text analogy, this is similar to deciding that to be detected as a cat, it has to start with a "c". So now you've discarded
In this way, it's not possible to ensure (notice the word) that your model will detect all of these unknown variations. There will be always some room for error that needs to be accepted, as long as the errors are infrequent or rare enough that they can be accepted as a regular part of the model.
Act III: Concept drift, a cautionary tale
Finally, the problem becomes even harder as we might be dealing with concepts that change over time, outside of the knowledge of the model, and outside of the knowledge of the person that supervised the model learning.
As and the breeds of cat changes, your model will have to accommodate by what we (users of the model) consider a valid definition of cat. Which might change in really unexpected ways and not really "look" like a cat. And since your model can only learn from what "looks" like a cat, it's always held in a disadvantaged position.
This will happen with almost any machine learning model that is approximating a result, regardless of the technique/algorithm. Approximations include a level of error because reality is usually complex in ways that we either don't know about or that are too computationally expensive.