How do game updates affect their ESRB rating and labels?

The ESRB has recently introduced new labels In-Game Purchases and In-Game Purchases (Includes Random Items). I think this is a move in the right direction, as it provides a warning label for gambling addicts who would otherwise be predated upon by these games (and who serve as the primary revenue stream for many unethical developers).

My question is about what might happen if a developer decided to introduce such mechanics in their game via an update some time after release. When an update is made, it is necessary in principle to have a third party review the changes and update the game's rating accordingly. I'm not saying this actually happens in practice.

My question is whether this actually takes place. Are games rerated when an update is released? Are devs required to declare whether their game may need rerating? If it does, are they charged for this? Do existing physical retail copies of the game have to be recalled and rebranded with the correct rating and labels? What are the limitations on the changes to the rating that an update can make? One would assume that a game rated for Everyone (E) cannot be updated to contain Adult Only (AO) content.

Finally, what about the ESRB listed interactive elements such as In-Game Purchases? Can they be safely ignored by developers updating their game to, e.g. include Loot Boxes or to suddenly require internet access?

According to the FAQs on ESRB's website:

How does the ESRB rate downloadable content (DLC) or other content updates that supplement a game or app?

Downloadable content (DLC) often refers to additional content that supplements or extends a previously-rated product. In most cases, the rating assigned to a game also applies to its DLC. However, if the DLC content exceeds the rating assigned to the “core” product, it must be submitted, and a different rating may be assigned to the DLC.

Should the ESRB find DLC or other update that is incompatible with the original rating, the developer and appropriate digital storefronts will be notified of a change to the rating for the DLC or, in the case where the update is required, a rating change for the core product.

Have games ever been re-rated? Yes. Take grand-theft-auto-san-andreas as an example. The ESRB re-rated it from Mature to Adult Only (a rarely seen rating) after the discovery of the controversial "Hot Coffee" scene:

On 20 July 2005, North America's organisation who establish content ratings for video games, the ESRB, changed the rating of the game from Mature (M) to Adults Only (AO), making San Andreas the only mass-released AO console game in the United States. Rockstar announced that it would cease production of the version of the game that included the controversial content. Rockstar gave distributors the option of applying an Adults Only ESRB rating sticker to copies of the game or returning them to be replaced by versions without the Hot Coffee content. Many retailers pulled the game off their shelves in compliance with their store regulations that kept them from selling AO games.

As to your last point about Interactive elements, I would think that would fall under a DLC or update, to which the ESRB would do as their FAQ states, and notify the developer that their rating has been changed/updated. However, for physical games (as in ones you would buy physically at a store) it is much harder to change ratings. Luckily, the market is much more digital that physical now a days, so this is a very small issue, if one at all.