If your pension plan is underfunded, you could be at risk of losing some of your benefits. That isn't news. But did you know that your pension can be at risk even if the plan is relatively healthy?

Something as seemingly innocuous as having a lump-sum payout provision, or even having a religious affiliation, could mean your benefits are vulnerable. Here are some red flags to look for, and some ways to protect yourself.

Your pension is healthy, but your employer isn't.

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Two years ago, the musicians at the San Francisco Symphony Orchestra got a rude shock when management, concerned about endowment losses, told the symphony board they should freeze the musicians' pensions.

Sound familiar? This is happening in workplaces around the nation, but in many cases managers who want to freeze pension plans are choosing financial assumptions that make the pension look like a bigger burden than it actually is.

Charlie Hill

The musicians hired an actuary, who challenged the assumptions that management was using and determined the pension wasn't that costly after all. As a result, management backed off.

"You have to push back," says Dave Gaudry, a viola player on the musicians' negotiating committee. "Don't believe what anybody says."

Your plan offers lump-sum payouts.

Many plans allow departing workers to take their pension benefits as a one-time payout instead of a monthly payment in retirement. It doesn't necessarily hurt the plan if a lot of people take their money out at once. All things being equal, when the plan pays out $100 million in lump sums, the obligation also falls by $100 million, so it's a wash.

It's a different story, though, if the company offers early retirement or separation incentives paid with plan assets, as opposed to using general corporate funds. If that is the case, a pension plan can quickly become underwater.

And this can affect your own ability to take a lump sum later on. If the plan's funding falls below 80%, federal law limits lump sums to 50% of the benefit. If the funding falls below 60%, lump sums are prohibited and the plan is automatically frozen, meaning your pension stops rising.

So keep a close eye on your plan's health if your employer begins a big downsizing push that includes enhanced pension payouts.

Your company changes hands.

Your pension plan might be fat and happy, but if another company takes over your employer—and your pension—it can legally use the assets in your plan to top off an underfunded plan of its own. This strategy, though legal, is one of the quickest ways for your pension to go from healthy to distressed.

Similarly, if your company spins off or sells your division, plan for the worst. Many companies spin off underperforming divisions, loading them up with retirees but without adequate assets to pay their promised benefits. Most retirees of Delphi, General Motors's GM +1.31% General Motors Co. U.S.: NYSE $34.53 +0.45 +1.31% March 17, 2014 2:55 pm Volume (Delayed 15m) : 21.20M P/E Ratio 8.86 Market Cap $54.20 Billion Dividend Yield N/A Rev. per Employee $709,712 03/17/14 General Motors Recalls 1.5 Mil... 03/16/14 Alibaba Plans Equal Sway for B... 03/15/14 Australia's Liberal-National C... More quote details and news » auto-parts spinoff, lost between 20% and 40% of their pensions when their plan was terminated in bankruptcy.

When Motorola was planning to spin off its mobile-device business in 2010, it planned to leave its pension plan, covering 87,000 people, behind in the old business. The Pension Benefit Guaranty Corp.—the quasifederal agency that insures pension plans—raised concerns, and early last year the company agreed to put $100 million into the plan over five years. A Motorola spokeswoman says the contribution was on top of the normal funding requirement.

Your employer gets religion.

Over the past decade, more than 100 employers—including hospitals, schools, nursing homes, universities, clinics and religious charities—have been claiming their pension plans are actually "church plans," a largely unregulated pension category that generally covers clergy and lay employees of churches, synagogues, mosques and other houses of worship.

Church plans are exempt from federal pension rules, including those that require employers to fund the plans and insure them with the PBGC. This puts participants at tremendous risk.

Employees at Augsburg Fortress, a publisher in Minneapolis that sells books published for the Evangelical Lutheran Church in America, lost 30% to 60% of their pensions when the publisher, which claimed the pension was a church plan, terminated it in 2010. Augsburg didn't respond to requests for comment.

Last fall, the Internal Revenue Service said employers must notify their employees and retirees if they are seeking church-plan status. But the rule isn't retroactive, so if your plan has converted already, your employer doesn't have to notify you. If you are worried, ask your plan administrator if your pension is protected by the PBGC.

What if you are a priest, pastor, rabbi or other employee and are in a genuine church plan? Pray for the best, because your employer isn't required to fund the plan, disclose much about its health or purchase insurance.

Write to Ellen E. Schultz at ellen.schultz@wsj.com