ok if it's a user who exists in a windows group, and doesn't have an individual login in SQL, then it's the issue Gazareth identified;
I assume the user are connecting with an application; that application has built a connection string with either a misspelled or non existent database in the connection string;
An example connection string:
Dim mySqlConnectionFormat As String = "data source=DEV223;
initial catalog=SandBox;
Trusted_Connection=True;
Timeout=600;
Workstation ID=GhostInTheMachine;
Application Name=HaxxorPadPlusPlus;"
so Following what Gazareth said, you need to track down how the connection is built, and get the app to fix it, i'm thinking.
Lowell