- A natural marriage between* two unbaptized people* can be dissolved by the Pauline Privilege if one of the party leaves the other to become a Catholic themselves and intend to marry a Catholic who also is free to marry.
- A natural marriage between a baptized person and an unbaptized person could be dissolved under the Petrine Privilege. This is a longer process based on my information.
Note that neither the Pauline or Petrine Privileges are annulments
per se since there is nothing to nullify.
To nullify implies that a sacramental bond was reviewed and then determined as lacking in something that invalidates that marriage. Unbaptized people don’t have a sacramental bond to their marriages,