At some point of Sekiro: Shadows Die Twice, Emma the Physician will disappear from Dilapidated Temple. Luckily, you won't have problems with finding her.
Emma goes to another place after the defeat of Genichiro Ashina. From now on she will stay near the main building of Dilapidated Temple. You can reach her fast - start in the temple, and then follow the path that leads to a small cave. The picture above shows the place where you can find a secret passage (rotating wall). Hug the wall and then press the interaction button.
The hero reaches Kuro's Room in Ashina Castle. Emma is here. You don't have to go from the temple to the castle every time you want to visit Emma - a Sculptor's Idol is in Kuro's Room.