Hello,
No, there is no relationship other than they're hosted from the same RDS hostname.
Did you delete a username that was used to access one or more databases?
It sound like the unused database may actually have been used.
Double check your code for any references to that deleted database name.
Do you have any backups or restore points configured so you can launch an RDS from a couple days ago, point to that, and see if your application starts working again?