It’s always good to think of the likely scenario before spending too much time searching a record set for a person.
I was looking for an individual in the 1840 US census. At the time of the enumeration the individual would have been over seventy-five years of age.
Part of my research plan needs to include the possibility that this individual is not enumerated in their own household. They could be living in the household of a child and not named as a head of household.
I should not rely entirely on indexes to find this person–a manual search of their likely area of residence should be conducted. But before my search for them strays too far from the probable residence, I should consider the possibility that they are enumerated in the household of one of their adult children.
And not named as a head of household themselves.