What once seemed like a worst-case scenario for Major League Baseball — a regular season of roughly 50 games — now appears to be all but inevitable.In yet another round of sharply worded statements and correspondence on Saturday night, the players’ union rejected the league’s latest salary proposal and essentially dared the league commissioner, Rob Manfred, to impose the severely shortened version of the season he has threatened.“It unfortunately appears that further dialogue with the league would be futile,” Tony Clark, the head of the players’ union, said. “It’s time to get back to work. Tell us when and where.”The strained relationship and the lack of trust between M.L.B. and the union have been on full display during their talks to begin the season after the coronavirus shutdown. While other major professional sports leagues, including the N.B.A. and the N.H.L., are further along in their resumptions, M.L.B. and the players’ union are still mired in a nasty public feud, volleying accusations of bad-faith negotiations back and forth.None of this bodes well for their immediate or distant future, with the collective bargaining agreement between the sides due to expire after the 2021 season.On Saturday, the union’s chief negotiator, Bruce Meyer, sent a letter to his counterpart at M.L.B., the deputy commissioner Dan Halem, declaring that the union believed negotiations over the 2020 season were at an end. Meyer blamed M.L.B.’s repeated insistence on pay cuts that go beyond a March agreement between the two sides, which stated that players would be paid a prorated salary depending on how many games were played and that the sides would “discuss in good faith the economic feasibility of playing games in the absence of spectators.”That pact allowed M.L.B. to set the new 2020 schedule and declared that the league should use its “best efforts to play as many games as possible, while taking into account player safety and health, rescheduling needs, competitive considerations, stadium availability and the economic feasibility of various alternatives.”But as it became apparent that any games would most likely have to be played without fans, M.L.B. owners repeatedly sought further pay cuts for players, who have held firm on the issue of receiving their full, prorated salaries. The latest offer from M.L.B. came Friday, calling for players to make 70 percent of their prorated salaries over a 72-game season — with the possibility of reaching 80 percent if the playoffs are completed.After the rejection of M.L.B.’s latest proposal, players expressed their exasperation and solidarity with the union on social media, with many echoing the union’s message: “Tell us when and where.”M.L.B., which interprets the March agreement differently, has argued that the shutdown has cost it billions of dollars already, and that games without fans would cut into revenues even more — thus the demands that players take additional cuts. The players’ union has asked for and said it hasn’t received sufficient documentation from M.L.B., which earned more than $10 billion in revenue last year, to support its financial claims.The union’s counterproposals have called for more games — as many as 114 — than M.L.B. has offered, with full, prorated pay. But the league desperately wants to protect its lucrative postseason revenue by wrapping up the World Series before a potential second wave of coronavirus infections in the fall, and to avoid a cluttered television sports schedule in November.M.L.B. has also sought an expanded postseason format, which would bring in more revenue, but that requires approval from the players.Last week, the St. Louis Cardinals owner Bill DeWitt Jr. said in a radio interview that “the industry isn’t very profitable, to be honest,” a claim that players resoundingly criticized given the billion-dollar values of team franchises and large television contracts. In his statement, Clark, the union chief, alluded to owners crying poor and to reports of a new M.L.B. national television rights deal. (Sports Business Daily reported on Saturday that M.L.B. had reached a new, larger extension with one of its rights holders, Turner Sports, worth $3.29 billion from 2022 to 2028.)If M.L.B. is indeed going to set the 2020 season, which the March agreement allows, Meyer asked M.L.B. to tell players how many games would be played, and when and where to report for work. “It is unfair to leave players and the fans hanging at this point, and further delay risks compromising health and safety,” he wrote to Halem. “We demand that you inform us of your plans by close of business on Monday.”In its response late Saturday night, M.L.B. said it was “disappointed” that the players’ union “has chosen not to negotiate in good faith.” The league once again argued that the March agreement was “premised on the parties’ mutual understanding that the players would be paid their full salaries only if play resumed in front of fans” — a characterization the union disputes.M.L.B. also said that the union’s position on pay “is not fair to the thousands of other baseball employees that clubs and our office are supporting financially during this very difficult 2020 season.”It concluded: “We will evaluate the union’s refusal to adhere to the terms of the March agreement, and after consulting with ownership, determine the best course to bring baseball back to our fans.”While M.L.B. could still come back with another proposal, and the union could file a grievance over a proposed season from M.L.B., Meyer’s letter on Saturday closed by addressing more immediate unfinished business.He said that while M.L.B.’s latest proposed guidelines for the 2020 season — which cover such matters as health protocols and rules governing the rosters — included the union’s feedback, several items needed to be ironed out further. “We will be available at your convenience to continue discussions on the manual,” he wrote.A season, even one under much disagreement, may be coming soon, after all.