baby farm
n.— «Among many of the phrases used to describe her for her despicable crime, the 33-year-old was called a “baby farm” because she appeared to deliberately increase her brood to gain more state aid.» —“Reforms hark back to roots of the welfare state” by Laura Devlin EDP24 (Norwich, England, United Kingdom) Dec. 11, 2008. (source: Double-Tongued Dictionary)
Further reading
Eels, orts, and Wordle! Sweden awarded its most prestigious literary award to a book about…eels. The Book of Eels reveals the mysterious life cycle of this sea creature and its significance for famous figures from Aristotle to Sigmund Freud. Plus...
At a South African boarding school, Rob picked up a phrase from Afrikaans that translates to land with your bum in the butter, meaning “to be lucky.” There are several variations in English — often with other words for “bum”, like...
I’ve heard the word “baby factory” in this context but never baby farm.