In March, Stephanie Jones, a single mom in West Chester, Pa., with an 11-year-old son, had several conversations with her employer about child-care concerns while schools were closed because of the novel coronavirus pandemic. According to a lawsuit filed April 16, she asked higher-ups at Eastern Airlines, where she worked as director of revenue management, if she could have two hours a day of flex time to focus on her son amid the long hours and weekends she was working.

Jones alleged that after a human resources official said her options were to take leave or resign, she asked about taking leave under the Families First Coronavirus Response Act. The official responded with an email that said he was “also well aware of the various new laws that you’ve had time to look up while at home” and that the law was “there as a safety net,” the lawsuit alleges.

Three days later, she was terminated, allegedly due to a “conflict” with other employees, which Jones denied.

Jones’s case, which was reported by Bloomberg Law, was one of the first known lawsuits under the Families First Coronavirus Response Act, which aims to expand paid sick leave and family medical leave to help vulnerable workers deal with schools and child-care centers closed because of the novel coronavirus, among other things.

(Jones, through a lawyer, declined to speak for this article. Emails sent to Eastern Airlines and its executives were not immediately returned. Eastern’s website says it is offering “relief flights” from Central and South America to Miami and mentions charter services.)

Yet it may be a sign of things to come as working parents — particularly mothers — struggle to manage work and child care.

“I’m one of these that believe that when the courts open back up, there’s going to be an explosion of coronavirus-related litigation, and this is just one piece of it,” said Cynthia Blevins Doll, an attorney with the firm Fisher Phillips who represents employers.

Christine Dinan, senior staff attorney for A Better Balance, which operates a help line about work and family legal issues, said some callers said they had been denied leave or paid time off for child care. As workplaces open back up, “those tensions are really going to be on prime display,” she said.

For now, many workers may be focusing on health concerns and fear retribution if they complain in an environment of record unemployment claims. Other employers, particularly those with workforces that have more easily translated to working from home, may have been more flexible as employees cope with shuttered schools and the pandemic.

But as things go on, some anticipate parents — especially women — will confront biases connected with family caregiving responsibilities that could result in more legal action.

“As school closures continue, the fragile safety net people have cobbled together will start to fray,” said Alexis Ronickher, a partner at the firm Katz, Marshall & Banks, which represents workers. “My expectation is we’ll start to see a lot more problems for caregivers and very much expect them to have a disproportionate effect on women.”

Under the Families First Coronavirus Response Act, workers at employers with fewer than 500 employees are eligible for up to 12 weeks of paid sick leave and expanded family and medical leave at two-thirds of their regular pay. The provisions apply through the end of 2020. (Businesses with fewer than 50 employees may qualify for an exemption).

The law created new forms of paid leave that employers are not accustomed to managing, Doll said. With new laws going into effect quickly, she fears some employers may misread employees’ requests and deny the leave, not realizing they could be violating the law.

Marianne Cooper, a sociologist at the VMware Women’s Leadership Innovation Lab at Stanford University, said that for many, the pandemic has increased the burdens on women for household and child-care duties. “All the different systems that women across the class ladder rely on to help them with that greater burden are gone overnight.”

Under federal anti-discrimination law, parents are not a protected class, although some state and local jurisdictions have certain protections. Federal courts have, however, made the connection between family caregiving responsibilities and sex discrimination, legal experts said.

“If you fire someone because of an assumption that she’s not a valuable worker because she’s a mother, that’s gender discrimination,” said Joan Williams, a law professor at the University of California Hastings who directs the Center for WorkLife Law. She said employers should look carefully at the demographics of their layoffs and whether layoffs include a disproportionate number of mothers or parents.

Some have said the pandemic could be an equalizer, shifting expectations for household responsibilities between men and women and making the “invisible” work of child care more apparent as managers struggle with schooling their own children and kids popping up in Zoom calls becomes the norm.

“The optimistic view is that we’re finally going to change our view of the definition of the ideal worker,” Williams said. “The pessimistic view is we’re going to have an avalanche of lawsuits as we discriminate against adults with caregiving responsibilities.”