Memento mori.
A language is dead when it is possible to know everything about it that exists to know. There are no new native speakers being born, no vowel shifts and consonant drift, no slang being coined, no idioms and memes developing daily and disappearing faster than they can be documented. All extant samples of the language, by its original native speakers, are recorded, analyzed, and used as teaching materials for non-native learners of the language.
A dead language can be contained in (whatever remains of) its entirety by a single mind, without that mind knowing the language as a mother tongue, but only as a professional academic interest. One may not be merely an expert in a dead language; one may be a definitive authority on it, knowing every conceivable word that is documented of it, as well as every inflection that could additionally be inferred based on that language's morphological rules.
Some languages are revenants, zombie languages resurrected in a "corrupt" form, for the use of specific communities as a primary unifying method of communication. Latin thrives within the Catholic Church as a shambling echo of its former, living self; what life it once had - productivity, novelty, originality - has survived in its descendants and their illegitimate cousins. Its vocabulary remains fixed and finite; it does not gain new words naturally as a simple fact of its continued existence. Communities of native Latin speakers are not born; they do not retain Latin as their primary language, in preference to a local lingua franca.
Some languages are undead, lich languages which cling to the jagged edge of life through the studious use of oral history. Sanskrit lives on in Vedic chanting, a system of recitation so aggressively and exactingly precise that the same tones and vowels survive thousands of years later, performed identically by individuals thousands of miles apart from each other, even as local living languages have drifted so dramatically as to be mutually unintelligible. The task of comprehending the meanings of these syllables is considered secondary to the task of preserving their sounds, which are regarded as sacred far beyond their semantic purpose. These chanters are no more native speakers of Sanskrit than any Cardinal is a native speaker of Latin, but the voice of Sanskrit is never lost.
Language is intrinsically memetic; it transmits virally between carriers. Carriers die, and language dies with them, slower but as inevitable as every form of cultural evolution. The growth of new modes of expression is as lovely as the loss of old modes is tragic, and there is a nobility (as much as a nostalgia and romanticism) in our refusal to let them disappear completely. Perhaps we deny them a graceful departure, when we do this, but it is uncontestably a very human response to loss.
Excluding their literal hundreds of inflections, Latin has thirty-three words for "kill" and seventeen words for "die." Latin only has one word for "completely forget." The magic of dead languages is that somehow, sometimes they survive their own deaths - always altered, always missing important pieces - but they survive nonetheless.
Ne obliviscaris.