They'd have to prove the oil companies caused a problem that would not have existed otherwise.
Much of this 'problem' is predicated on model predictions of climate change, something proven time and again to be profoundly inaccurate as a prediction device, and models which appear to be flawed, amidst doctored data which have been 'adjusted' to show higher temperatures. The combined effect of adjusted data and flawed models is to yield predictions of change, but a century or more in the future. A preemptive suit for damages which may not ever be realized?
Take that precedent to the ambulance-chaser level, and any driver could sue any other, predicated on the possibility of a future accident.
In short: there is no proof of climate change that can be attributed solely to these oil companies, in fact, if the models were correct (an assertion I will NOT make), other energy sources might have released far more of the very gasses being blamed for what temperature and /or sea level rise. Sea level change can be accounted for by natural mechanisms, if it turns out the sea went up and the land did not go down.
Did the sea level rise or the city sink? In an area which has been subjected to high seismicity and has areas prone to liquefaction, has any study been done to ascertain whether the problems are compounded by or exist solely as a result of earthquake activity and tectonic alteration of topography and bathymetry? How about aquifer drainage, what effect has that had on elevations? Have other coastal cities dropped in elevation relative to mean sea level and what mechanisms might be causing that, aside from the assertion by folks who have failed to predict long term climate changes so far that this time, they have it right, not just right, mind you, but so right they want to extract money from the pockets of every motorist using these models as a justification.
What are the contributions to sea level changes of calving glaciers, constructed islands from Dubai to the Spratleys, and tectonic events such as the displacement of the Boxing Day Earthquake or the one which wrecked Fukushima? How has submarine volcanic activity altered the capacity of the ocean basins, especially in areas where new oceanic plate is formed on an ongoing basis? What proof that any documented change is the result of climate and not other factors? What part does the sediment load transferred to those ocean basins through landmass erosion play in seal level change? Surely, all these factors alter the capacity of the ocean basins. Maybe climate is not at fault, after all.
Lastly, should the suit find a sympathetic (if unscientific) judicial ear, these corporations should immediately cease selling any petroleum products there, and let 'em walk.