Customer reported that they couldn't add any new users to site. UI error message was as follows:
 

Unable to add <email>
We couldn't send your invitation. Try inviting that user again

The network response has more information:

{"key":"noDefaultGroup","context":{"message":"No default group for Product: Product{productId=jira-software, workspaceId=<xxx>, cloudId=<xxx>} and Role: JIRA_SOFTWARE_MEMBER"}}

The related issue ID-8067 - Admin page allows removing default product access shows how it is possible for a site to get in a state where it has no default access group.

Workaround

Go to https://admin.atlassian.com/s/<cloud id>/apps and choose a default access group for Jira: