Explain the concept of closures that do not go out of scope in programming.

In programming, a closure is a function that captures and retains references to variables from an outer scope, even after that scope has finished executing. The concept of non-outliving closures means that the closure continues to have access to these variables because they are not destroyed as long as the closure exists.

For example, in Swift:

func makeIncrementer(amount: Int) -> () -> Int {
    var total = 0
    return {
        total += amount
        return total
    }
}

let incrementByFive = makeIncrementer(amount: 5)
print(incrementByFive()) // 5
print(incrementByFive()) // 10

Here, the closure retains the variable total, which would normally go out of scope after makeIncrementer is executed. But thanks to the closure, total is preserved and modified with each call.

Thus, closures allow for maintaining state and working with variables from outer scopes without leaving them.