There are people who put limit orders on the exchanges. Say that the price of TSLA is $500. I think it's overpriced, and its likely to go down, but then grow in the future. I can say, "I'm willing to buy 100 shares of TSLA at $420." Someone else holds TSLA and thinks its likely to go up, but not hold it's value, so they say, "I'm willing to sell 100 shares of TSLA at $690." The sum of all of these limit orders forms the market depth chart.
The more common way to interact with the market is to say, "I want to buy a share of TSLA at the current market price." In the above example, the only option is to buy TSLA for $690, even though the last transaction was $500! This is a example with very little market depth. In the normal case, you'd buy your share for $500.02 or something like that. (Same, but reversed, for selling at market price.)
For more information, but with a crypto focus, see https://hackernoon.com/depth-chart-and-its-significance-in-t...
For your example, you would put in a market order, and buy the stock at the lowest price that someone was willing to sell it at. If the last price was $4, but the lowest limit order that currently existed was for $100, and you bought it for $100, then yes, the price would go up to $100. (In real life, those sharp upticks don't happen much. It's more likely that a sharp downtick happens, where suddenly everyone wants to sell oil futures at the same time, but almost no one is willing to buy them, so the price ends up negative.)
Note that whenever people defend high-frequency trading for "providing liquidity to the market," this action of setting buy and sell limit orders that are close to each other is what they are talking about. There are algorithms that will see TSLA at $500, and offer to sell TSLA at $500.02 and buy TSLA at 499.98. If both orders go through, they make $0.04. If you operate fast enough to get out ahead of any big market moves, you can make a lot of money. But if you ever accidentally buy a bunch of TSLA for $499.98 right before the price plummets to $420, then you just lost a lot of money. This is why HFT and other trades with similar risk profiles are sometimes referred to as "picking up nickels in front of a steamroller."