The term was mentioned in, “The Valachi Papers”; 1968; Peter Maas. It seems to refer to a cheap insurance coverage for poor people. It was used mostly in the late 1920s and early 1930s and was a part of the Black Market. The Mafia ran the racket to make a little extra money, although they most likely hired Jew actuaries of the time.
The Penny Insurance seemed to pave the way for, “playing the numbers”, which was seen as not being very different in nature. It was said that, “playing the numbers was just like taking out a cheap policy.”
I don’t have much further information on the Penny Insurance business, but it probably was a big part of the New York business for the poor people. The insurer would guarantee money if a certain event occurred, such as an accident of some kind. But what the events that were covered for Penny Insurance are unknown.