You don't necessarily completely lose the ability to hear at a given frequency.
Thanks to healthy surrounding cells.
Often times you just lose a fraction of your ability to detect sound at that frequency.
Due to loss of cells at that frequency or very close to it.
That's what you measure with a hearing test. If you get a threshold of 40 dB at 1 kHz it means that you haven't lost all the ability to hear 1 kHz, but you need that frequency amplified by 40 dB to make it "sound like normal" again.
A 1000 Hz tone does not exclusively stimulate the 1000 Hz section of the cochlea. It rather stimulates a range of frequencies in the cochlea, perhaps from 900 Hz to 1100 Hz. You perceive this as a 1000 Hz tone, even if you have missing hair cells at exactly 1000 Hz. This is possible because the brain is smart enough to predict the highest peak to be at 1000 Hz by using the information from the surrounding hair cells. A 40 dB hearing level at 1000 Hz is like a mean average hearing level for frequencies ranging from 900 Hz to 1100 Hz, centered at 1000 Hz.
If hearing a frequency was exclusively binary you'd have very weird looking audiograms zig-zagging all over the place.
Well it's not binary. One reason is because outer hair cells are innervated by spiral ganglion neurons in bundles of 15 or more hair cells. For 1 neuron you have 15 outer hair cells. That's not binary (in the sense of one on one correspondence)! I am not even accounting for the inner hair cells. The second reason is the way that fluid/mechanical waves propagate inside the cochlea. This is all the more reason why the cochlea is such a complex organ.
There is no reason to believe that there is a one on one correspondence between test tone pitches and the cochlea. This is exactly why you don't see the graph zig zagging (unless you have severely damaged cochlea). The audiograms show mean average hearing levels at pitches one octave apart: 250, 500, 1000, 2000, 4000, 8000 (plus the half octave 6000) Hz. That's why we don't need to do the test with 1 Hz increments to get an idea of the hearing level. Such test would take at least two hours to complete, if not more. If you were to do such a tedious test you might see the kind of zigzag graph you describe.
In many cases, you still have enough cells, synapses, and whatever else is required in the pipeline to hear the frequency range partially.
Frequency ranges, yes. But also discrete frequencies, with the help of surrounding healthy cells within the range. In other words, if all your cells and synapses are dead at 1000 Hz, you will still be able to perceive 1000 Hz tones if your hair cells 100 Hz below and 100 Hz above that are healthy and alive. This way you can hear all the frequencies in the range 900 Hz to 1100 Hz. But you will have the classic "dip" at exactly 1000 Hz.
The "dip" is more or less evident on the graph, i.e. more or less shallow and sharp. The deeper and sharper the dip, the more severe the damage is at that test frequency. But this can be elusive. The dip can be shallow and dull. So it depends on the sampling of the test. You need more sampling frequencies and more sampling points to tell how far-spread the damage is at the cochlea. The standard hearing test consists of 7 sampling frequencies. You will need more than that. The standard hearing test is a good gauge for overall hearing level. But it cannot serve well as a way to assess this kind of granular hearing discrepancies and to give us detailed information about the cellular damage in the cochlea.
A visual tool, such as a µOCT endoscope would serve that purpose much better. Not to mention how much faster we could assess the damage, compared to doing insane 1 Hz increment audiometry. A visual instrument like that is something we are currently missing in the clinics.
The last point I want to make is that if the range at which you have cellular damage is wide enough, you will not be able to hear certain frequencies within that range, least of all the mid frequency. If the cells corresponding to the range 500 Hz to 1500 Hz are all dead, I bet you can't hear a 1000 Hz tone! As you get closer to the endpoints of that range you may start to hear some tones. So you may be able to hear the 800 Hz tone, as well as 1200 Hz tone, but maybe only after increasing the volume to 50 dB. At the very endpoints you would most certainly be able to hear the tones, assuming you don't have any other damaged segments below 500 Hz or above 1500 Hz. So you may hear the 500 Hz tone, perhaps at mild to moderate 30 dB level.
We may not know the details of how and why it happens, but the tests are repeatable, consistent, and do show that it happens.
Not sure what to make of this... how or why what happens? I may have already answered this... if you're referring to why we still can hear certain frequencies at some level, even after damage to the hair cells or the synapses in a certain region of the cochlea.