A mummified language is one that is still in active use in some context but it is no longer anyone’s birth language.
In Europe, the archetypical mummfied language is Latin: It was the language of the Roman Empire, split and mutated into the Romance languages when the Dark Ages made travel difficult, but was preserved by the Roman Catholic Church as a liturgical language until the present day. Words have been added so the RCC can discuss television and airplanes in its Latin-language dispatches, but the language itself has not changed as, say, Italian has.
Another example is Coptic, the last linguistic descendant of the ancient Egyptian language (that is, prior to Greek and Arabic, the language of the heiroglyphics on the pyramids) which is the liturgical language of the Coptic Christian Church.
The final example I’m sure of is Hebrew, which isn’t mummified any longer. It was the language of the ancient Hebrew kingdoms, became a mummified liturgical language during the Jewish Diaspora, and was revived in the late 1940s to become the national language of Israel. (To be explicit, it ceased to be mummified when a child learned it as his or her first language.)
Are there any I’m missing? I don’t know about Sanskrit for two reasons: A constructed language cannot be mummified, and it might be a first language for some people in the village of Mattur. Modern Standard Arabic seems to not be anyone’s first language, but I don’t know if it qualifies as its own language and I don’t know if it isn’t artificial.