If it's an ETF it's a little complicated. The usual mechanism for selling an ETF is that there's a buyer on the other end who's buying shares in the ETF itself, not the constituent stocks. Arbitrage keeps the price in line with the index constituents; if the ETF diverges from its constituent assets, some HFT can buy the ETF and sell the constituents and that will force them to converge.

However, most ETFs are also setup such that they can create or destroy shares in response to large shifts in demand. In this case, if enough people hit sell, the ETF itself will buy back shares and use the proceeds to sell the underlying assets, in a transaction that mechanically should be market-neutral and just propagate the supply/demand of the fund down to the individual stocks.

With Vanguard specifically, it's even more complicated, because VTI is not a separate ETF. It's a share class of the Vanguard Total Stock Market Index Fund. But the mechanism is largely the same - it has the same Authorized Participant system to mint new shares in case of high demand and redeem shares if everybody sells, and then passes these requests on to the underlying mutual fund, which can then piggyback on some of the tax efficiency benefits of the ETF.