The documentation string you provided at the top of the module would better be placed in the function, and the examples should be formatted as doctests so that they can automatically be checked.

The control flow can be simplified and manual handling of indexes eliminated if you iterate directly over the input list, maintain a `deque` for the currently considered subsequence, and use an inner `while` loop for discarding numbers.

    from collections import deque
    
    def contains_subsequence_sum(numbers, target):
        '''Given a sequence of positive integers `numbers` and an integer `target`,
        return whether there is a continuous sub-sequence of `numbers` that sums up
        to exactly `target`.
    
        >>> contains_subsequence_sum([23, 5, 4, 7, 2, 11], 20)  # 7 + 2 + 11 = 20
        True
        >>> contains_subsequence_sum([1, 3, 5, 23, 2], 8)       # 3 + 5 = 8
        True
        >>> contains_subsequence_sum([1, 3, 5, 23, 2], 7)
        False
        '''
        subsequence = deque()
        total = 0
    
        for number in numbers:
            if total < target:
                subsequence.append(number)
                total += number
            while total > target and subsequence:
                total -= subsequence.popleft()
            if total == target:
                return True
    
        return False

The original name `sum_target` suggests that the function returns a number when it actually returns a boolean value (it is a *predicate*). Such functions tend to have names like "has", "is", "contains", etc. While I'm still not quite happy with it, the name `contains_subsequence_sum` is a better fit.