Yes, employers can and should pursue performance management strategies, although when someone declares a disability they need to take that into account in the implementation of the strategy.
For example, in LolaSmiles's example of a teacher making errors in marking and reports and parents complaining... Yes, of course this should be approached as per performance management policy although if someone discloses that they're dyslexic (or have another disability) the next step should be to adjust for that disability eg have someone proof read, more time to write reports, maybe writing feedback online with a spell checker and printing out etc etc.
This should be regularly reviewed and adjusted if need be.
If someone doesn't disclose a disability (either because they don't have one or don't want to) the next step would likely be being sent on some sort of training and some targets for improvement.
The organisation could have have addressed things sooner ie when errors started emerging rather than leaving it a couple of terms, and given someone a chance to disclose a disability then.
It's the individual's responsibility to disclose their disability and the organisation's to manage performance promptly.
In reality, it's usually systemic rather than individual problems that cause a delay in performance management, eg 1:1s being postponed due to workload, hazy performance management policy, managers not being trained/feeling confident in implementing it.
No, it doesn't always work like this in the real world, which is called disability discrimination and not the fault of the individual.