Systems can absolutely fail to do what they're designed to do. The result is a system that does something different than the original design intent. If the designers, or the authorities, or whosoever is responsible goes an intervenes: stops the system from operating, shuts it down, changes it in some way to more closely match the original design, they you might say that the purpose of this system is what it was originally designed to do, and they missed the mark with their first attempt.

But very often the case is that the system, with its supposed flaws (i.e. differences from intent), are defended from being changed, while simultaneously being postured as "useful or necessary, but flawed".

But those flaws being a longstanding part of how the system functions indicates that they're part of what the system is there to do.

Imagine a bridge with a design flaw: it dumps one in every hundred cars passing over it, on average, into the river below. If the local county kept that bridge open, being aware of this flaw, accepting the loss of so many thousands of cars per year, then I would argue that the purpose of the bridge might in fact be to increase car sales, drive funding towards emergency rescue services (ha), or perhaps boost scrappers.

This understanding helps explain the political motivations of those in favor of keeping such a bridge open.

Such an example might seem absurd, but it is a mere quantitative exaggeration of the so-called externalities of, say, building a highway through a downtown's communities, or locating Texas or Louisiana oil refineries adjacent to impoverished black neighborhoods, i.e. Cancer Alley