That depends entirely on how cheap the alternatives are. Fossil fuel mining is not zero cost in itself, so there is a minimum price it can’t go below.
Indeed, quite a lot of coal plants are being shut down — they can’t compete as the fuel itself is too expensive. This is not universal as not all coal is the same price and transport costs are also relevant, but it is happening.
If that’s what you’re quoting (I’ve not seen any recent attempts to calculate the costs of oil extraction), each barrel has ~1.7 MWh of energy. By way of comparison, PV solar records are around $0.02/kWh = $34/BOE.
That's not how markets work, at all. Oil has an extraction cost, and once the price falls below the profitable threshold, the production will absolutely shutdown.
This highly visible with the boom/bust cycle of the more expensive extraction areas (dakotas, canada, etc).
So as demand continues to drop due to competition from cheaper energy, oil supply will start to collapse as well because none of it comes for free and taking it out of the ground will become a money losing proposition.
This is untrue. If cost to extract >> market price, then existing operations may well just be shut down. To quote Hemmingway it would likely happen "gradually then suddenly".
First, if we have clean energy, are we going to shut down fossil fuel plants that have already been built? If not, then fossil fuel will just become cheaper as demand drops, making burning fossil fuels attractive again. Countries currently plan to reduce their emissions, but none are planning to reduce their fossil fuel exports. They just hope it will show up on another country's emissions balance sheet.
Even if we did develop super cheap clean energy, that would only reduce emissions in the future. Past emissions hang around for centuries and contribute to warm the planet (https://www.theguardian.com/environment/2012/jan/16/greenhou...). We would need to pay huge amounts to sequester that CO2 and I don't see anybody volunteering to foot that bill.
This paper summarises both issues well: https://journals.plos.org/plosone/article?id=10.1371/journal...
Both are just aspects of the fundamental issue - although technological solutions perhaps could be developed, there is no political or economic will to do so, and no indication that will change.