I'm not sure about Terraform, but Pulumi has an options object that can set parameters about how Pulumi interacts with that resource. I tend to enable `protect` on database resources which prevents Pulumi from deleting it.

AWS has done a great job at making it difficult-to-impossible to tear everything down in a single command. There are rate limits on resource deletion and no single place to remove items in bulk if not managed by Cloud Formation. I spent the better part of a couple days trying to clean up an account from all of the random supporting services that get created over the years. If I'm wrong about this, please let me know!