Do you mean the title of a topic? Posts aren’t updated automatically for that, but you can use the Rebuild HTML button in the post wrench if you come across one. The links still function correctly though even with a title change.
(If you did want to find them to update/rebuild HTML the posts they’re linked in should also have a backlink inserted at the bottom of the post)
For quotes, it would be unusual to automatically change those as it could drastically change the meaning of what the user was referring to when they quoted it. They’re more useful as a quote of what was said.
(Just as an extra bit of info, a Featured Link is a different feature in Discourse than links included in posts. A Featured Link is one where you paste a link into the title box when creating a new topic and it embeds the link in the title area when published)