@oristarA,
oristarA wrote: The problem for understanding the grammar is that "their" and "them" (in "that a person with asthma or hypertension, for example, would have faeces posted through their letter box to scare them away from the neighbourhood") all refer to "a person with asthma or hypertension").
You need to be aware of the "singular they'. This is the use of they (or its inflected forms, such as them or their) to refer to an entity that is not plural, or not necessarily plural. Though singular they is widespread in everyday English and has a long history of usage, debate continues about its acceptability. It typically occurs in these situations:
Indeterminate gender:
This is when they refers to an individual person of unknown or unspecified sex, as in, for example, "One student failed their exam". This usage is known as epicene they.
Indeterminate number:
Used when they has no definite antecedent, or can be interpreted as referring to either a singular or plural entity. This usage is also known as generic they. For example, in "Anyone who thinks they have been affected should contact their doctor".
In some cases, they is used even when both the number and gender of the subject are known, but the identity of the person is generic, e.g. "If some guy beat me up, I'd leave them."