The PGA has no say over the PGA Championship field either -- it is owned by the PGA of America. The PGA owns/controls no majors. Somebody posted some stuff on the other board about tour membership regarding the PGA championship,, but it was irrelevant.
Those entities, except maybe the Masters, I suspect have no interest in lawsuits from players on LIV either.
What will matter for some on the LIV tour will be what happens with world golf rankings for their events because Top 50 in the world gets you in any major (typically 60's or the British and up to 90's at times for the PGA Championship) . This might be the best way for the PGA to block the "Upper Midcard" from leaving - think guys like Kevin Na, Talor Gooch, Patrick Reed (non Masters), Lee Westwood, Ian Poulter. They will have a hard time playing enough events to stay in the top 50 or even top 100 for too long. But it might not be that effective to block a player currently in the top 20 especially if they have a recent major.
The problem is the top (Dustin Johnson, Bryson Dechambeau, Cameron Smith) are just starting or fairly early in 5 year exemptions to all majors due to winning one. Patrick Reed has one more year. There are also exemptions for past winners, top 12 in prior year, and top 5 in any major the prior year.
And it will take a while for somebody in the top 15 now to drop out of the top 50 (or 80 for the PGA) -- they still have the majors, 2 WGC's, and some asian tournaments to help them if needed. They will certainly fall, but they should be able to maintain a spot for a few years (say a player like Hovland left).