Murriny Patha is fun. Especially if you like "kintax" (Evans 2003), cause it's got it in spades. Murriny Patha keeps delivering weird phenomena that require unconventional nomenclature (see for instance Walsh 1996). "So what", I hear you asking, "is the 'elided progeny' construction?" In Murriny Patha it constitutes a subclass of what are clearly a group of "triangular" referring expressions, whereby a person-referent is referred to via "triangulation" - that is indirectly, via another person or persons. The most common of these are possessed kinterms: my father, your uncle, their cousin etc. The person that the kinterm is anchored to is frequently termed the propositus. Other classes of people may also take a propositus: e.g., John's bank manager. Arguably all kinterms are anchored to a propositus, regardless of whether the propositus is expressed overtly or not. Thus when an adult addresses a child, "Hey, where's daddy?", the altercentric kinterm Daddy has an implied 2nd person propositus. However the same adult, when talking to another adult, may use egocentric kinterms with an implied 1st person propositus i.e., "Mum is driving me mad."
The "elided progeny" construction is a kind of kin-based triangulation, but the kinterm corresponding to son or daughter is just missing. These things are very common in Murriny Patha conversation. In fact "triangulation" is generally a very common means of referring to people. I wouldn't say it's the default method of referring to persons, but it probably is the preferred choice for "upgrading" reference to persons. So how does this construction work? It's basically a special case of the Murriny Patha possessive construction.