Since you do not mention a specific piece of literature, I expect you are referring to the paradoxical pairing of "ignorance and strength." We generally assume that strength comes with knowledge. However, when a paradox is presented—a statement that at first seem self-contradictory and untrue—it does not mean that it will never make sense: we simply need to look at it in a different manner. It is important to remember, too, that ignorance does not necessarily refer to stupidity, but to a lack of knowledge.
In terms of paradox, we see them in Shakespeare's Macbeth—one of the themes is "fair is foul and foul is fair." This line comes from the three witches at the beginning of the play. The comment means "good is bad and bad is good," which sounds impossible. How can something good be bad? This is a paradox. The answer is that something can seem good while really being bad, and something can seem bad while really being good.
Macbeth seems like a valiant and loyal follower of the King, but secretly kills him. Also, when the witches deliver their first set of predictions to Macbeth, they seem very positive, without any sense risk or danger, but actually lead to his death. Both are examples of "Fair is foul…"
At the same time, when the King's sons run away, it looks as if they are guilty of killing their father, but in truth, they don't want to be murdered like their father was, and leave only for their protection, an example of "Foul is fair…"
Regarding the question of how ignorance can be strength is found in Bret Harte's short story, "The Outcasts of Poker Flats." A small group of people is banished from Poker Flats because they are perceived as undesirables. They stop to rest along the way to the next town, but as they sleep, their mules are stolen by one of the members of the party—creating dire circumstances for the rest of the outcasts, especially when it begins to snow. However, a couple from the neighboring town arrive—Simson and Piney—who are eloping, traveling to Poker Flats to marry.
The young people are protected physically and emotionally by these outcasts so that Simson and Piney are not aware of the danger they actually are in. At one point, it is Simson's ignorance that lends him courage to go out to bring back help.
One of the women, Mother Shipton, has stopped eating, wanting her rations to go to Piney—and she dies. Oakhurst, the gambler from Poker Flats, does not tell anyone of her passing, pretending that she is merely very sick. He tells Simson that her only hope of survival is that young Simson travel to Poker Flats and bring back help, which he agrees to do—while Oakhurst chooses to remain behind to help the women if he can.
Invariably, sending Simson on his way saves his life: he goes on his journey to save someone else. His ignorance of Mother Shipton's true condition gives him hope and strength that he might save her if he is willing to put himself in jeopardy.
In this way, I can see that ignorance helps one to be strong. Not being aware of the dangers or uncertainties one may face can provide someone with the strength he or she needs because there is no perception of danger or uncertainty to create fear.