Allow me to clarify by starting with the opening paragraph of the Wikipedia article on "Proto-Indo-European language":
No direct evidence of PIE exists – scholars have reconstructed PIE from its present-day descendants using the comparative method. For example, compare the pairs of words in Italian and English: piede and foot, padre and father, pesce and fish. Since there is a consistent correspondence of the initial consonants that emerges far too frequently to be coincidental, one can assume that these languages stem from a common parent language. Detailed analysis suggests a system of sound laws to describe the phonetic and phonological changes from the hypothetical ancestral words to the modern ones. These laws have become so detailed and reliable as to support the Neogrammarian rule: the Indo-European sound laws apply without exception.
So in a different world, a language spoken by a particular population underwent a similar path but diverged into a language that sounded nothing like its ancestor. What sorts of circumstances could make that sort of evolution possible?
No alien involvement, magic or total extinction scenario, thank you.