Theoretically it may be possible to do a complete search of all of the possible records for finding your ancestors, but in practical terms, it is highly unlikely that anyone has actually achieved a "complete" search. For example, my Great-grandfather lived in a small town in northern Arizona for his whole life. The town, currently called Joseph City, never had more than about 1,500 or so people. It is not listed as a U.S. Census area and is an unincorporated community. Do you think you could find all the records of genealogical interest for this small town in Arizona?
Let's say you went back to the 1920 U.S. Census when my Great-grandfather was living in what was then called St. Joseph. Do you think that he knew virtually everyone in that small town? Let's say further that you have searched all of the following types of records:
U.S. and State Census records
Land and Property Records
And you thought you were doing a pretty good job of searching for information about St. Joseph/Joseph City. But did you search all of those types of records and search in all of the City, State and University libraries in Arizona. Would it surprise you to know that the Cline Library at Northern Arizona University has at least five major collections of records from early residents of St. Joseph/Joseph City and that one collection, the George S. Tanner collection has 9 linear feet of records? Contained in those records is a Diary of John Bushman that mentions my Great-grandfather on almost every page. How far would your search for records go? Did you look in the University of Utah Library and the Brigham Young University Library? Both of these libraries have huge collections of documents and diaries of genealogical significance about my family and St. Joseph/Joseph City. Both of those university libraries happen to be in Utah, an adjoining state.
When I did a search in the BYU Harold B. Lee Library catalog I found many more linear feet of documents about the town and people who knew my Great-grandfather. What about the Arizona State University Library, the University of Arizona Library, the Arizona State Library, the Utah State Archives, on and on and on. How long do you think it would take you to look in all those libraries and look through all those documents?
What if my Great-grandfather had lived in New York City or Boston or Philadelphia? How many more records would I have to search? By the way, have you visited the Philadelphia City Archives? They have birth records, city directories, death records, deeds, marriage records, naturalization records, court records including divorce records, insolvency petitions and bonds, support bonds, apprenticeship indentures, tax assessment registers, street lists of voters and other records.
Do you begin to see what I mean when I say that it highly unlikely that anyone has actually exhausted all of the possible places and records that could exist about one individual, much less and entire family. But you claim, your ancestor was poor, obscure and could neither read nor write, he or she left no records. But what about all the family's neighbors, friends, church members, the lists go on and on.
What I find, most of the time, when people claim to have searched all of the records, it means they don't know about any other records. In a town like St. Joseph/Joseph City, I would submit that a complete search of the records would include a search in every library in Arizona and Utah for records on every single person showing on the Census records for all of the years who lived in that town and every other record about each of those individuals.
Is this something we want to do? Or even care about doing? Probably not, but don't complain if I happen to disbelieve you when you claim to have searched everywhere. Is there some compelling reason to search all those different records in all those different places? That is a question you have to answer for yourself but in the meantime, don't claim that you have searched all of the possible records until you really have done so.