This summary is not the rule. The rule text controls.
If an insurance company based in Louisiana goes into receivership, meaning a court has appointed someone to take over and manage its affairs, that appointed receiver becomes the correct person to sue if you're trying to enforce a claim or obligation against the company. You wouldn't sue the insurance company directly anymore. Instead, your legal action needs to name the receiver as the defendant.
The rule also covers insurance companies based outside Louisiana (whether in another state or another country) that do business in Louisiana. If one of these "foreign" or "alien" insurers ends up in receivership and Louisiana has appointed an ancillary receiver to handle matters here, that ancillary receiver is who you name in your lawsuit. This applies whether you're trying to enforce an obligation of the insurance company itself, or an obligation of either the main receiver overseeing the company elsewhere or the ancillary receiver handling things in Louisiana.
In practical terms, this rule tells you who to name as the defendant when an insurance company you're dealing with is no longer running its own affairs because a court has stepped in. Naming the wrong party could cause delays or problems with your case, so it matters to get this right based on where the company is based and who has been appointed to manage it.