We have the same issue as well: everything works as it should for almost all users, but for one specific user, noone can assign issues to this specific user, her name does not show up in Assignee dropdown list in the new issue view. All other users can be found in the list, but not this specific user. If we switch to the old view, the user can be found and assigned as usual.
In the new issue view, the user can be found in the Reporter dropdown list and can be selected here.
The user can work in Jira as usual both in new and old issue view.
The permissions for the user is exactly the same as other users that we can assign to in the new issue view.