Several Zygons adopted the identity of Petronella Osgood at various times. Part of a group stuck on Earth, these Zygons landed in 1562, but the group retreated into a stasis cube and stayed there until the 21st century. At that time, one Zygon took Osgood's form after ambushing the real Osgood and took her inhaler. Osgood escaped, reclaiming her inhaler while doing so.
Later, three of the Doctors erased the memories of both the humans and their Zygon counterparts when they took control of the UNIT Black Archive, and peace was restored. When this Zygon suffered an asthma attack in Osgood form, the real Osgood quietly passed over her inhaler, allowing these two to secretly know which was human and which was Zygon. (TV: The Day of the Doctor)
The two Osgoods then created Operation Double, where a group of 20 million Zygons would be allowed to live on Earth and take on the form of the nearest person they could find. The treaty could only be maintained if both humans and Zygons agreed to live among each other in peace, and that no harm would come to anyone. They were given a device called the Osgood Box by the Doctor, to be used only in a dire emergency. (TV: The Zygon Invasion) However, one of the Osgoods was killed by Missy. (TV: Death in Heaven)