The use of the U. S. Federal Census or any of the state censuses conducted in-between the each decade of the federal population count are a wonderful source of data about our ancestors. It is a way to gauge who was living with their parents, ages, occupations, property values and birth places. Following each decade that an ancestor lived is a mini history of their life.
So when a researcher examines a census where they can not locate their ancestor there is great annoyance and frustration. This is true whether the researcher knows for sure the relative did live beyond the census date or if they are uncertain if the person had died since the last census.
There can be several explanations why an ancestor might be located. First, they moved to another county or state and the researcher is not expanding the search location. Second, during the date of the census count the individual might have been visiting friends or relatives in a totally different place so they were counted in their host's household and not with their own home.
An important part to remember about the census records were that they were handwritten by the census enumerators and they could have made mistakes in spelling or even writing the correct given and surname names of an individual. Then later when the censuses have been transcribed, whoever examined the handwritten name could have misinterpreted a name. The census records and transcriptions do have many errors so a researcher has to become creative in their quest.
For a female ancestor the search becomes more difficult when you do not know a married name. The birth surname is known and the female was followed up to about age 21 in the 1870 census, now the researcher can not locate them under that maiden name in the 1880 census. Start by locating the parents and then examining the neighbors. Many times a young couple will set up housekeeping near her parents. If not the parent then near an uncle or an older brother. Check the known relatives and then go house to house from each to see if the missing female relative is located. Compare the given names, the age, birthplace and parent's birthplace. If you find a possibility, make a note of her married name, the husband's full name to then compare with any marriage records.
Another method to help find an elusive ancestor is by searching in a given location using just their given name and approximate birth year. Now if the name is John or Mary, there could be many names to go through, but quite a few times this is how an ancestor is finally found.