I'm in the oil business. Here it is in a nutshell, specifically the upstream part of it. You spend a bunch of money to drill a hole where you've estimated how many barrels of oil you'll be able to pull out of that hole. That's your capital cost. Then it costs money to actually pull the oil out of the hole and get it to the buyer. That's the operational cost. You can survive for a while if you're just covering your operational costs, it's just that no additional holes are going to be dug.
By and large, you can't just "turn off" an oil well like it's a faucet. So all this oil that's come into the market that isn't being consumed has to go somewhere. Right now storage is historically tight and expensive, and that's why the price of oil went negative. As some of tweets mentioned, you may find yourself in a situation where you have to take possession of the oil, but you can't find a tank, railcar or ship to put it in.
The Exxons and Shells of the world are integrated meaning they can take the oil they drill and do stuff with it like make gas, chemicals, etc., but they can't move any of that stuff right now and they're running out of space too. Bottom line, until we reopen up the economy, this is going to be a big problem.