As any good union official or lawyer will tell you; it entirely depends on their employment contracts and jurisdiction of that contract.
Simply put: If literally all the players refuse to play in the ESL but continue their commitment to play in the officially licensed competitions, I would, as a complete layman, contend they would have a massive collective bargaining case against the ESL clubs.
The ESL would withold wages but this would literally be challenged under Employment Law UK and EU wide.
Have the players signed up as employees or private contractors?
What is the contract between them and their clubs in terms of the expected service the players provide?
Can the ESL clubs withold full salary or terminate contracts for not participating in an unsanctioned league if the players continue to abide by the contract of playing in licensed competitions?
Better yet, if ever there was a time to form a players and managers pan-global workers union it should and would be now.
If there is a will then there is a way. Would be immense.
No-one has mentioned the players; No players = no ESL.
The players can go on a strike. There will be litigation and most likely it will fall flat.
I've seen a standard Premier League player contract and it stipulates that a player has a obligation to partake in any competition the club takes part in if ordered by a club official.
The contracts stipulates several points that are listed as breach of rules with list of penalties, up to and including termination of contact.
If a contract is terminated by rulebreach, the club can, and as we know with these owners, will go after the players for not the wages, but their
transfer value. The players values are listed as club assets.
Chelsea did this in 2004 v Adrian Mutu after his cocaine verdict.
Players banding together vocally in an illegal protest after litigation would mean that they technically can run the risk of being in breach of contract by "putting the club in ill repute"
Now, there is literally years of litigation, arbitration and public opinion between a first complaint and a conclusion to a lawsuit, but that is the worst possible outcome.
The best outcome is that the PFA is successful in protecting the players right to not take part in a competition that will damage their domestic league, and sport in general. I'm sure that is an argument that they will make.
There have been player strikes before, and could be again. But we really need someone to be brave here.