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Which one is accurate?

...when one or two individuals do not have [an ID] or [IDs]

another example:

...this is the case when one or two students [are] or [is] missing

Theoretically, if one individual is missing, then it's an ID (first eg), and it should be "are" (second eg). We don't know, so which one should we choose?

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When a verb has two or more subjects connected by or or nor, the verb should agree with the last-named subject. Thus,

...when one or two individuals do not have IDs

(You'll note that you already used the plural form of the verb, "do" in this example)

and

...this is the case when one or two students are missing.

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