This summary is not the rule. The rule text controls.
When an insurance company gets taken over by a court-appointed receiver, this rule spells out who has the legal right to file lawsuits on the company's behalf. If the insurance company is based in Louisiana, the receiver appointed by a Louisiana court is the one who can sue to collect debts or enforce the company's legal rights.
If the insurance company is based in another state or country but has assets or business in Louisiana, things work a bit differently. In that case, Louisiana courts can appoint what's called an "ancillary receiver" to handle matters here. This ancillary receiver has the authority to file lawsuits in Louisiana to protect the company's rights or the rights of the main receiver handling the company's affairs elsewhere.
The rule also clears up what the word "receiver" actually covers. It's not just one specific job title. It includes anyone acting as a liquidator (someone who sells off the company's assets), a rehabilitator (someone trying to fix and restore the company), or a conservator (someone protecting the company's assets during a crisis). This matters because it means the same rules about who can sue apply no matter which of these roles the person holds.