PARIS — L’Oréal’s stock climbed steeply during Friday trading, a day after the death of Liliane Bettencourt, the sole child of the company’s founder, was announced, triggering speculation about what changes her passing might prompt — if any — in the relationship between the Bettencourt family and Nestlé.

The two parties, which comprise the beauty-maker’s largest individual stakeholders — with 33.05 percent and 23.3 percent, respectively — have a shareholders’ agreement that is unlocked six months after her demise.

The principle terms of that pact outline that neither party could increase its stake in L’Oréal during the lifetime of Bettencourt and in the six months after her death. That means starting in March, the parties no longer have to work in concert. (Each has been free to offer its shares to any third party since April 2014.)

L’Oréal shares surged more than 6 percent during Friday trading before closing up 2.5 percent to 180.95 euros. Meanwhile, Nestlé’s stock gained 0.2 percent to 80.55 Swiss francs, or $83.

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Analysts outlined a few main scenarios that could unfurl including: the companies maintaining their status quo, L’Oréal buying back Nestlé’s stake, or Nestlé either upping its share in the beauty giant or acquiring the company outright. The first and second possibilities seem the most likely to investors.

In describing the case where nothing happens for a long while, Jeffries equity analyst Martin Deboo wrote: “The concert agreement will now lapse. But what might not lapse is the spirit of cooperation between L’Oréal and Nestlé, and their mutual long investment horizons.”

Another theory is that L’Oréal buys back the stock from Nestlé, partially financed by the sale of its 9.4 percent stake in Sanofi.

Pinar Ergun, an analyst at UBS, sees it unlikely Nestlé will increase its share in L’Oréal or purchase the company. “Nestlé’s new ceo has commented publicly on a number of occasions…that he is focused on small- [and] medium-sized deals,” Ergun wrote. “In February, he stated that he wanted to ‘dissuade any concerns here that we would resort now to big-ticket deal-making,’ noting that valuations were too rich.”

Nestlé’s chief executive officer Mark Schneider also underlined that the coffee, pets, waters, nutrition and consumer-health segments were of strategic focus, highlighted Ergun.

Nestlé has already in the recent past pared down its L’Oréal holding. In a multistep transaction that closed in July 2014, the Swiss company trimmed its stake from 29.4 percent.

Nestlé has been feeling increased pressure regarding L’Oréal since this summer, when activist investor Dan Loeb began pressuring the group to divest its holding in L’Oréal, calling it nonstrategic.

Céline Pannuti, European consumer goods analyst at J.P. Morgan Cazenove, raised another scenario, given the mounting pace of consolidation in the personal-care industry and beauty’s strong fundamentals versus other staples segments.

“As far as Nestlé’s interesting in buying, we believe that at a time of portfolio reshuffling within the industry, a potential takeover of L’Oréal by Nestlé cannot be discarded completely, although we would expect this to be determined by Nestlé’s [long-term] vision and structure,” she wrote in a note.