tl;dr – Some of these bugs are not like the others
Here's hoping you've enjoyed playing with trucks and bowls and your imaginations. If we're going to be able to use our model as an illustration of much value , we have to recognise that in relation to software testing it contains a useful approximation, and a misleading lie.
There's a limited collection of things to find. This can be a useful approximation for exploration in software testing – if one assumes that a system has a finite collection of possible behaviours, then the set of possible but undesirable behaviours is limited too (as compared with the vast set of rubbish things that it doesn't actually do). This is good to consider when told "there's always a bug" by an idiot*.
You might further refine this by adjusting your view from the large mass of observably rotten behaviour to the smaller selection of practical changes that make the system more desirable. You'll also recognise that the collection, while limited, is only fixed if everything else is fixed. In our model, the collection of bugs is fixed – so we need to be clear that the approximation and the model assumes that, just of now, no one's changing stuff**.
The rate of finding things falls, as the number of things that can be found falls. This is obviously true, but is perversely also a misleading lie***. Idiots (sometimes, the same idiots who believe "there's always a bug") assume, because of the statement's obvious truth, that when the rate of finding bugs drops, the system is close to clean. Bonnnnng.
Sometimes, and it feels like often, it's because the people testing it have run out of imagination. While we may understand more as we reveal more, and while a system may become cleaner as it gets fixed, a dropping bug rate certainly does not imply you've found all the bugs.
Some testing is done by an unbending list of dull asserts, which run clear and green when they've not managed to either trigger or observe any trouble. Michael Bolton reasonably calls these "checks" rather than tests. Some testers, limited by corporate focus or personal blandness, don't do much better, demonstrating simply**** that a system meets expectations.
As any fule kno, some bugs are harder to find than others. If you find you've run out of bugs, it's likely you've run out of bugs that you're set up to find. Sometimes, that's OK. But sometimes, a bug that's hard for you to find is easy for someone else to find. If that someone else isn't a paid tester, but is heaven forfend, a paying customer, we get the "why didn't you find that" conversation.
So, then. A couple of approximations for this model.
1 Some bugs are harder to find than others.
I'll model this by giving some bugs a high chance of being found, and other a low chance. The way that easy-to-hard works amongst the bugs is called a probability distribution. We can pick a distribution. Our earlier example, the trucks and bowls, would be a fixed, or flat distribution, where everything has the same chance, because we assume that trucks/bowls are effectively equal within the model. That's the stupid but easy assumption that lies under the misleading lie. Bugs are different.
2 We don't have a find-fix-retest cycle in our model. Nothing is being changed.
This makes the model easier to understand, because we're not looking at two things going on at the same time. Of course it's inaccurate. The trick is to use the imagination to wonder how that inaccuracy might appear. Models should be visceral, so go with your emotion if you don't want to be analytical.
Finally, a wrinkle. Exploring is about learning. As we discover more, we get better at discovering, not worse. We start out rubbish, and one trick that distinguishes good testers is how quickly they get better (not how good they start). This leads us to
3 Everything's harder to find early on.
In our model, we have a tester. The chance of them finding any given bug starts at a particular value (0, say) and increases. In this model, it increases over time, and it's much easier to go from nothing to halfway good than it is to go from halfway good to perfect. There are lots of different ways of modelling this – again, use your imagination to think how the model might change.
So – here's a model of a tester discovering bugs. I've fixed it so that there are 400 bugs to find, but some are harder than others. The tester gets better over time.
* Not that they'll listen. Indeed, that's close-on the definition of an idiot, which is apparently from a Latin word meaning "ignorant person". Clearly they are, if they're ignoring you.
** I'm aware that this is impossible and in many ways undesirable in the real world. My model, my rules. Just making them explicit.
*** something to have in mind whenever someone says "obviously"
**** but oh, in such a complicated way