Premier League is a huge money maker for the country and supports 1000s of jobs so that was never stopping, even more so if it did clubs would have to pay back around £2bn in TV money.
IC and King's Lynn only want the season ending because there'll likely be no relegation, and as a result be nothing to play for. Nothing to do with players safety etc. Majority of league will still have plans to push for promotion, so I can see the league continuing. North/South will stop as majority are not chasing promotion at all costs, so will be happy to stop.