Crowdfunding campaigns have become the go-to funding option for more and more people who find themselves stretched by the costs of a medical crisis, whether that consists of uninsured health-care service or medical equipment, or related costs like making up for missed earnings. But not everyone is equally able to access this source of funding: The ability to raise money online depends heavily on how wealthy a person’s friends and other connections are.

For those who aren’t well off, it’s often hard to raise even a fraction...