In your stored procedure, make sure you rollback the transaction and raise error when it happens. This way the task will fail and the ssis package will fail and stop executing.
Begin Try
Begin Tran deff
Update [test].[dbo].[User2]
Set [Password]='abc'
Where [User_ID]='abc'
Commit Tran deff
End Try
Begin Catch
IF XACT_STATE() <> 0
ROLLBACK TRANSACTION
RAISERROR ('Transaction Rolled Back', 16, 1)
End Catch