The number of Americans buying self-defense insurance—dubbed “murder insurance” by critics who believe it can encourage the use of deadly force—has soared in recent years.

The insurers offer a range of services, including bail and criminal-defense lawyers. Some also cover the cost of litigating civil lawsuits brought by victims of the shootings. Upgraded plans can also include crime-scene cleanup costs, TSA-violation expenses, accidental-discharge costs and coverage for spouses and minor children.The fine print of their policies, however, shows the companies usually have wide latitude to reject a member’s claim.