The employer can give a reference that is truthful and factual, so he can say the employee has a bad record of timekeeping; has had x periods of sick leave in the past 2 years; has been warned about poor performance and so on - there will be records of this to back it all up.
He can also say in his opinion the employee would be unsuitable for the job as typist as the employee cannot reach the required typing accuracy and speed if there is a record of this.
He can't say he doesn't trust the employee and thinks he may be a thief, or may be workshy if there is no evidence to support it.
So yes, an employer can give a bad reference.
In my experience if the shoddy employee is still working for the employer, a good reference is given in the hope the employee will leave of his own accord.