Here's my attempt:

    # Multi-pass FizzBuzz
    n = 100 
    # [['1'], ['2'], ['3'], ['4'], ['5'], ...]
    seq = [[str(i)] for i in range(1, n + 1)] 
    # [['1'], ['2'], ['3', 'Fizz'], ['4'], ['5'], ...]
    for i in range(3, n +  1, 3): 
        seq[i-1].append('Fizz')
    # [['1'], ['2'], ['3', 'Fizz'], ['4'], ['5', 'Buzz'], ..., ['15', ''Fizz', 'Buzz'], ...]
    for i in range(5, n + 1, 5): 
        seq[i-1].append('Buzz')
    # Arithmetic equivalent to:
    # len=1 -> the whole thing (from zero to end, because zero = -zero)
    # len=2 -> the length-1 suffix (just Fizz or Buzz)
    # len=3 -> the length-2 suffix (Fizz and Buzz)
    # The branch is hidden in the slice syntax:
    # Python has to check whether `x` is negative in `terms[x:]`. 
    for terms in seq:
        print(''.join(terms[-(len(terms) - 1):]))

Here's a version that uses generators instead of multiple passes over a list:

    # Single-pass FizzBuzz
    n = 100

    def numbers():
        for i in range(1, n+1):
            yield [str(i)]

    def fizzies():
        nums = numbers()
        try:
            while True:
                yield next(nums)
                yield next(nums)
                yield [*next(nums), 'Fizz']
        except StopIteration:
            pass

    def buzzies():
        fzs = fizzies()
        try:
            while True:
                yield next(fzs)
                yield next(fzs)
                yield next(fzs)
                yield next(fzs)
                yield [*next(fzs), 'Buzz']
        except StopIteration:
            pass

    for terms in buzzies():
        print(''.join(terms[-(len(terms) - 1):]))

Edit: Can't resist -- unbounded without loops, but recursion blows the call stack (granted, well after 100):

    def numbers(i=1):
        yield [str(i)]
        yield from numbers(i+1)
    
    def fizzies(source=numbers()):
        yield next(source)
        yield next(source)
        yield [*next(source), 'Fizz']
        yield from fizzies(source)
    
    def buzzies(source=fizzies()):
        yield next(source)
        yield next(source)
        yield next(source)
        yield next(source)
        yield [*next(source), 'Buzz']
        yield from buzzies(source)
    
    def main(source=buzzies()):
        terms = next(source)
        print(''.join(terms[1-len(terms):]))
        main(source)
    
    main()