Oil briefly went negative a few years ago. If you decided to build a storage business dependent on negative oil prices for profit, you might just be coming online around now, and very much poorer than you were before. (Of course you would in fact have stopped a long time ago.)
There is good news though. With electric car sales slowing down (at least in the west) there is a surplus of batteries on the market, which makes grid storage projects more affordable. The incentives are currently pushing us towards decarbonizing our electric infrastructure faster and that is wonderful. As long as the politicians don't do anything dumb like slap huge tariffs on solar cells or something we should be making some real progress towards a green future.
But they do. Often literally.
Negative prices usually happen because of laws requiring minimum utilization, or subsides, or because they are so small and rare that it is not worth having someone on place to turn the switch.
Since we're being pedantic, as I understand it, the grid operators don't usually tell plants what to do (outside of system stress response, curtailment, etc), the grid operator shares the forecast, and when the price forecast is low, fossil fuel plants are likely tell the grid operator they'd rather shutdown than produce power at low/negative prices. For solar plants, there's no fuel cost, and there might be subsidies, so producing at a negative market price might still be positive for the generator and there's no reason to turn it off. For nuclear, fueling schedules don't really change based on use, so there's no reason to not provide optimum power outage other than for grid stability.
Grid scale storage should reduce price swings, since storage plants will tend to show up on the demand side when prices are low and the supply side when prices are high; although perhaps price swings will become bigger when prediction fails --- if storage fills up by noon you'll have a lot of excess supply until sunset; if storage empties by midnight, you may have a lot of excess demand until sunrise.