Where it says
..and when the whole Number of Widows shall be complete, 3 Annuitants will die..
it's intending to say
..and by the time the whole number of Widows becomes known for certain, 3 Annuitants will die..
They use the phrase "shall be" rather than "is" in part because they're making a prediction; they're talking about something that hasn't happened yet. (They're basing their prediction on what has happened in the past, but they're making a prediction, nonetheless.)
They use the phrase "shall be" rather than "will be" because they're preferring an older and more formal style, and maybe to reduce the number of times they use the word "will" in the same sentence.
At the time and place when and where this was written, I believe, as another contributor mentions, the word "shall" may have carried a connotation of certainty and finality that the word "will" didn't quite; so they're basically saying
"By the time we actually know for sure how many Widows were left, 3 Annuitants will have died."
I would say that even in modern usage, even in America, the word "shall" still carries a slightly greater degree of certainty and finality than the word "will." But it's not commonly used, and it sounds kind of old and formal.