Connie Willis's novel Doomsday Book imagines a future in which historians do field work by traveling into the past as observers. History seems to have built-in protections to keep the past from being altered by preventing travelers from visiting certain places or times. In such a case, the time machine will refuse to function, and no trip is possible. Some other destinations are technically feasible, but the authorities deem them too dangerous to visit.
A young female historian, a specialist in medieval history, persuades the authorities running the project to send her to England in the 14th century, a period previously thought too dangerous for anyone, much less a woman. She will be the first historian to visit the period, and is well prepared, she thinks, for what she will encounter.
At this point nearly everything that could possibly go wrong does. The technician who set her coordinates collapses as an early victim of a deadly new influenza epidemic which shuts down the project. The time traveller herself comes down with the infection almost immediately after arriving in the past, but because her immune system was enhanced prior to her jump, she survives. She awakens after several days of fever delirium to find herself being cared for by people who soon discover that she is literate. Literacy is so rare among women that they decide she is almost certainly a runaway nun and intend to pack her off to a convent, whether she's willing to go or not, as soon as possible. Worse yet, during her delirium and wanderings she lost track of the physical location where she arrived. She must somehow find it and hope to be there when the door opens again -- if it ever does.
The book switches back and forth between her situation and the pandemic going on in the present. There are interesting, well-drawn characters in both eras.
One last detail: the already-feverish technician back at the project sent her to the wrong year. She has arrived in England just as the Black Death is starting.