A subname is a name under another name, like pay.yourname.eth. The name above it is the parent. A parent controls a subname through roles on its registry and resolver. Some parents keep those roles. Others give them up.
Getting a subname from someone? Check who else holds a role before you rely on it.
Open the subname in ENS Explorer and go to its Roles section.
Read every list: Parent registry, Registry-wide roles and the resolver's own list.
If an address other than yours holds Unregister, it can delete the name. Upgrade lets it change the name.
If a project gave you the subname, such as yourname.base.eth, you usually register, renew and edit records on the project's own site. See What are project subnames?.
A subname's expiry can't be later than its parent's. If the parent name expires, its subnames stop resolving.
Related: What are project subnames? · Subnames