I think you misunderstand. This is when serving things before not working as it should.
Example server 6:
If a city has not hit 1000 population yet then you can have thousands of wood going there but the wood counter has not yet been created. So, we get to say 20 February. The town now peaks over 1000 population for the first time. Now the wood counter is created. At this time town info will show 0/x of wood required. you only have 8 days to fill the quota. Everything that was collected before was sent to /dev/null, before the counter was created.
If the city pops over and back down then that is fine and the counter remains. This is all shown by the requirement counter on the town info screen. At the top of the town info it says 30 days grace.
I'm pretty sure i've seen players deliberately demolish buildings after new requirements as a workaround. But is is not supposed to work that way.