Most Americans assume if a loved one or breadwinner is killed or seriously injured on the job, insurance — at the very least, the workers’ compensation insurance that states generally require employers to carry — will help with the resulting expenses.

But a pair of recent cases cast doubt on whether this system is working the way most participants expect.

Retired 26-year Las Vegas police sergeant Stan Cooper, 72, was working as an armed and uniformed security officer at the Lloyd George U.S. Courthouse in downtown Las Vegas, sitting in a chair near the metal detector when a disgruntled federal benefits claimant walked in and killed him with a shotgun blast on Jan. 4, 2010.

Yet Mr. Cooper’s son Marty was advised last month that his claim for payment under the 1976 federal Public Safety Officers’ Benefits Act had been denied, the Justice Department in Washington ruling “Claimant has not established that Court Security Officer Cooper was a public safety officer serving a public agency in an official capacity at the time of his death.”

Because Mr. Cooper was not married, no one is receiving his pension. His son also says no one in the family is eligible for any workers’ compensation benefits related to his death. “Every time we turn around, everything is just completely denied.”

In a separate and perhaps more outrageous case, we also learn this week of the plight of Mark Lindquist, 51, whose survival is considered a medical miracle. He has been honored as “a true hero and inspiration to others” by both houses on the Missouri legislature.

Mr. Lindquist, who earned slightly above minimum wage, felt he couldn’t afford medical insurance. But he would surely appear to have been “on the job” as he watched the skies darken on the evening of May 22 while driving to the Joplin group home where he was employed as a social worker, helping three middle-aged residents with Down syndrome.

The tornado sirens began to blare. Because there was no basement or shelter and the three residents moved too slowly to relocate, Mr. Lindquist and co-worker Ryan Tackett placed mattresses over the men, and then climbed atop the mattresses to add their own weight to the makeshift shelter.

More than 7,000 homes were destroyed. Sadly, the three men Mr. Lindquist was trying to protect were among the 162 dead. After the storm, rescuers found Mr. Lindquist buried in rubble, impaled on a piece of metal. Large chunks of his flesh were torn away. The bones in his shoulder crumbled as he was placed on a stretcher. All his ribs were broken, and most of his teeth were knocked out. He was in a coma for two months and had been rendered so unrecognizable that it took three days for his family to locate him in an area hospital.

Though he still carries his right arm in a sling, Mr. Lindquist can use the hand. He can see and walk and speak. Doctors consider his recovery amazing.

But perhaps not as amazing as the fact that, while Mr. Lindquist has run up $2.5 million in medical bills, Accident Fund Insurance, his employer’s workers’ compensation carrier, has denied his claim “based on the fact that there was no greater risk than the general public at the time you were involved in the Joplin tornado.”

Yes, insurers have to examine claims closely, aiming to keep premiums down by rooting out frivolous filings or outright fraud. But if these two claims haven’t resulted in expected benefits being paid, why are employers obliged to pay premiums to “insurers” with money that otherwise could be handed to workers for use to buy their own, private coverage, or simply to salt away against a future time of need?