That's not true.
1) The title is can you win 800 million in powerball. If you passed 800 million, you win congratulations you did it.
2) It can be impossible to reach 0 even with a random walk.
I think you want to be more precise about "impossible".
It is not mathematically provable that a random walk of finite length will eventually touch 0. Proof by counterexample: the set of every walk of length 1 where you win the jackpot on your first try.
However, consider an infinite random walk. You can fix the first n values of the walk to win the jackpot as much as you want, but as the random walk progresses toward infinity, it is highly probable that you will be on a random walk that tends toward negative infinity. (You might have to play a lot; $437 million of $3 tickets would probably be enough tickets to play powerball for a few lifetimes.)
It is not mathematically provable that a random walk of finite length will eventually touch 0. Proof by counterexample: the set of every walk of length 1 where you win the jackpot on your first try.
However, consider an infinite random walk. You can fix the first n values of the walk to win the jackpot as much as you want, but as the random walk progresses toward infinity, it is highly probable that you will be on a random walk that tends toward negative infinity. (You might have to play a lot; $437 million of $3 tickets would probably be enough tickets to play powerball for a few lifetimes.)