The City Council has scheduled a closed-door meeting at 9 a.m. Friday to talk about an appeals court ruling that could cost Cambridge millions in lawyer fees, awards, court fees and interest.

The meeting will include a report from City Manager Robert W. Healy, who has driven the city’s unsuccessful attempts to thwart the wrongful-termination lawsuit, about “what he thinks the next steps are,” said councillor Marjorie Decker on Wednesday.

The appeals court weighed in Monday, saying “We have no occasion to disturb the judgment” of the lower court, but quotes from Healy and city solicitor Don Drisdell in The Boston Globe and Cambridge Chronicle said they were still reviewing that appeal decision, suggesting a further legal fight was possible in the 6-year-old case.

Estimates put the ultimate cost in Malvina Monteiro vs. City of Cambridge at more than $10 million, and cranky constituents have complained in public comment periods at council meetings that the city should have cut its losses years ago and saved taxpayers some money — a position Decker said she and fellow councillor Ken Reeves have supported vocally. “I’ve been very clear with where I’m at,” Decker said. “This needs to be settled and we need to move on.”

Two more cases like Monteiro’s are coming along, both represented by Monteiro’s lawyer, Ellen Zucker. One case arrives in court in mid-September for a pretrial hearing.

“There’s a lot of stuff here that has to be put on the table and discussed,” Decker said.

Constituents are now complaining about the closed-door and nontelevised nature of Friday’s meeting.

A closed-door, nontelevised meeting is “a violation of the very rules of the City Council the announcement says will apply, as well as the municipal charter, which guarantees citizens and employees of the city a reasonable opportunity to address the councillors on all matters that come before it for action during its open meetings,” said North Cambridge resident Michael Brandon, referring to a city announcement saying the meeting “shall be subject to the Rules of the City Council as amended.”

The council should have to call a meeting, with public comment, before calling a closed-door session, say residents such as Brandon. The amended rules of the council allow for “special meetings” to be called but don’t explain what a special meeting is. The rules of public comment are broken into two categories: regular business meetings; and regular round table/working meetings. That leaves the rules of public comment for special meetings not clearly addressed.

Litigation is generally considered cause for closed-door sessions, though, despite the language of state law muddying the reasoning by grouping it with union negotiations. Massachusetts General Laws let government keep the public out “if an open meeting may have a detrimental effect on the bargaining or litigating position of the governmental body.”

Closed-door meetings such as this are “not unusual,” Decker said. “Any discussion on this has been in executive session because it has to do with an active legal case. It’s not to block out the public.”

Messages were left Wednesday with Mayor David Maher and Henrietta Davis, a councillor and the vice mayor, for comment.

This post was amended Aug. 18, 2011, to clarify that residents believe the council should have to call a meeting, with public comment, before calling a closed-door session.