Is there any kind of science studying what History does not record?

The closest science which looks for more history as yet undiscovered falls into the category of anthropology.

There are two major branches to anthropology: Physical Anthropology and Social/Cultural Anthropology.

You may want to begin reading about this endeavour by researching the work of Margaret Meade.

There is this organism called "salmonella". This organism has been responsible for countless cases of food poisoning and even death over the centuries. The history of how this bug is responsible for so much suffering and of how mankind learned to avoid salmonella is pretty doggone important - because salmonella is still around and people still occasionally get sick because of it. Would you rather your parents followed you through life hollering at you to wash your hands and only eat well-cooked chicken and fish, or would you prefer to learn the history involved and why that's necessary for your good health and then be left alone to run your own life? Yo, there's hundreds of nasty little germs like that, and wouldn't you rather know the history of how people learned to keep from getting sick rather than experience those illnesses yourself? THAT's why history is important: you don't want to repeat it and learn the important stuff the hard way! One of those germs, which is still around and which still makes some people sick every single day, killed a third of the population of the world only a few hundred years ago. In fact, it did that more than once - it's the germ that causes Plague, the "Black Death". Or how about the ones that cause Malaria, the oldest known disease, which is still around? Or Hansen's Disease, also called "Leprosy"? Didn't know Leprosy's still around, did ya? The United States Public Health Service still runs a leprosarium - a hospital just for victims of Leprosy - in Carville, Louisiana. Wanna visit? I thought not. So study history and learn how to avoid catching Leprosy! How's them for good reasons to study history, dude?

If you want to know about what is not known in history, then the subject to study is history. For example, we don't know much about the Estruscans, so the thing to do is study Etruscan history more and find something new about them. It could be done partly through archeology and by deciphering the Etruscan language, which we have not been able to understand. Doing research into the holes in history is simply doing historical research. For example, Evans changed our understanding of early civilization in the Mediterranean by his excavations on Crete.

Finding out what is not known is called research. People do it all the time, especially scientists.

Maybe I don't understand what you are asking, but History is a field that requires documents as evidence to find answers. If it isn't written down, historians can't talk about it. History is sometimes viewed as a social science, but it is often grouped with the humanities, as it is here on Yahoo.

crypto-history

If you are looking for some biblical times history, look into "Apocrypha". These were books written at the same time as the ones in the common bible, but weren't accepted as mainstream to the people who put together the cannon we have today because of the viewpoints of the authors.