The only financing that happens with a stock is at the point of IPO, which is obviously not applicable for these ancient oil companies. I'm not sure an oil company has issued more outstanding shares for financing in a very long time. They get the vast majority of their financing through low-interest debt.
Public companies can issue more stock to public markets at any time. That stock would be priced at the market rate. If a company’s stock price tanks due to lack of demand, that is bad for the company. Similarly, companies with failing stock prices have problems attracting (and bleeding) talent.