By Shayndi Raice and Liz Hoffman 

At a heated meeting with Mylan NV's executive team in a Manhattan conference room in May, several investors complained about the drug maker's resistance to a $40 billion takeover proposal from Teva Pharmaceutical Industries Ltd.

Executive Chairman Robert Coury leaned across the table and retorted, in language laced with expletives, "This is a stakeholder company, not a shareholder company," according to multiple attendees, meaning his constituents went beyond investors and he wasn't obligated to agree to a tie-up.

Mr. Coury got his way. On Monday, frustrated in its monthslong pursuit of Mylan, Teva pivoted, saying it had agreed to buy Allergan PLC's generic-drugs business for $40.5 billion and was dropping the Mylan effort.

Mylan's resistance to Teva's proposal was aided by an acquisition that moved the company's legal home in February from Pennsylvania to the Netherlands--part of the wave of tax-trimming "inversion" transactions that swept American business last year. Mylan, whose senior management remain based in Pennsylvania, gained not just tax savings, but a Dutch corporate rule book that gives companies more levers to resist takeovers.

Mylan shareholders were left reeling Monday, as the stock fell more than 14% to $56.37, well below Teva's $82-a-share offer. Meanwhile, Teva shares added 16.4% to $72, a hefty jump for an acquirer, while Allergan shares rose 6.1% to $326.98 on news of the deal, expected to help it trim debt and focus its strategy.

The outcome for Mylan shows a consequence of the recent inversion craze, now becoming clearer as companies lay down roots in new jurisdictions.

As these companies begin to pursue deals, and get pursued, rules of the game are shifting for shareholders and management.

At some companies, like Mylan, shareholders now have less leverage with management thanks to their new foreign home, while at others, like Perrigo Co., which redomiciled to Ireland in 2013, shareholders are more empowered and companies have fewer tools with which to resist takeovers.

"Often participants look to inversions and see only the tax upsides," said Peter Lyons, global co-head of the M&A practice at law firm Freshfields Bruckhaus Deringer LLP. "Many times there's more to the analysis, whether it be different rules on corporate governance or differences in the approach to [future] transactions. They would be well-served to consider all of these factors."

A Mylan spokesman said, "Mylan certainly has always considered the interests of shareholders. But a core principle at Mylan is that shareholders benefit from a well-run business, and to run a business well, you need to focus on all of the stakeholders we touch on a daily basis, including customers, patients, employees, suppliers, creditors and communities."

Mylan has also maintained its stand-alone strategy is preferable to a takeover by Teva. Mylan primarily makes generic drugs but also sells the popular branded product EpiPen, a treatment for allergic reactions.

The Netherlands is a stark example of how the takeover rules can change. As U.S. companies moved to invert in recent years--buying a foreign entity and then switching domiciles-- most headed for Ireland or the U.K., where lower tax rates combined with language and cultural fits.

But Dutch policy makers have spent the past decade touting the benefits of Dutch law to global corporations as part of an effort to turn the Netherlands into a management-friendly bastion.

Advocates of the Dutch system say it lets boards invest in the business and plan for the long term, while critics say the balance tilts too far in favor of management over shareholders.

Rients Abma, executive director of Eumedion, an organization representing Dutch institutional investors, said he worries such moves "will give the impression among foreign shareholders that [the Netherlands] is not a shareholder-friendly environment and that can have negative consequences for all companies incorporated in the Netherlands."

Mylan set up a Dutch foundation, known as a stichting, which is an antitakeover defense comparable to a U.S.-style poison pill. The foundation had the right to receive preferred shares that allow it to block any deal, outvoting other shareholders. The board of Mylan's stichting triggered its special voting rights last week, saying it would oppose a takeover by Teva.

Mylan also instituted a rule that says only the current chairman--today, Mr. Coury--can appoint new directors, even in the event all board members are ousted by shareholders. That means shareholders effectively cannot replace the board, a powerful tool in U.S. takeover fights. Corporate-law experts said this provision would be highly unlikely to survive a legal challenge in the U.S.

That nomination right was spelled out in Mylan's disclosures to shareholders about the deal, which was approved by 97% of votes cast. Yet some investors are disenchanted with the reality: A lawsuit filed on behalf of Mylan shareholders in June in Pennsylvania alleges the company didn't give shareholders an adequate say over the creation of the stichting. A Mylan spokesman said the company believes suit is without merit.

Other companies are using similar strategies. Cable firm Altice SA is proposing its shareholders vote in August to switch its corporate domicile from Luxembourg to the Netherlands, a move that will allow it to institute a dual-class share structure. Such a structure, which is generally barred in Luxembourg, would give the company's chairman, Patrick Drahi, approximately 92% of the company's voting power while owning 58.5% of the company.

Similarly, Italy's Agnelli family was able to tighten its grip on Fiat Chrysler Automobiles NV when it switched its domicile to the Netherlands last year. The move allowed the family to increase its voting power to around 46% on a financial stake of about 30%.

As for Perrigo, currently facing a hostile takeover attempt from Mylan, the maker of private-label drugs redomiciled to Ireland through a 2013 merger and, in doing so, surrendered a bevy of takeover defenses that could now come in handy. Ireland has no poison pills and doesn't allow boards to take any actions, like large acquisitions or restructurings, to thwart a takeover bid.

That is good news for Perrigo's shareholders eager for a quick premium, but leaves its board with fewer options.

Perrigo shares rose 3.8% to $193.60 on Monday.

Write to Shayndi Raice at shayndi.raice@wsj.com and Liz Hoffman at liz.hoffman@wsj.com

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