If someone has less than one years service, they can be dismissed with notice ( normally one week's statutory notice) but if they have more than one year, the employer has to go through statutory disciplinary procedures before someone can be dismissed fairly. You can be dismissed whilst off sick if the employer has gone through statutory procedures and either consulted with the employees gp or take independent medical advice and asked the employee to undertake an independent medical examination.
If the person is disabled, then they are given protection under the law if they are dismissed purely because of their disability. They can however be dismissed because of capability, redundancy, conduct or some other substantial reason. Again statutory procedures have to be applied.
No employer is exempt from employement law but the Employment Tribunal will take into account the size and resources of the employer ie they will not expect the small shopkeeper to have the same procedures set up as say Marks and Spencer or Sainsburys. Neverthesless statutory procedures and discrimination law, especially disability, still apply.
For further advice either look at www.acas.org.uk or call the Acas helpline on 0845 47 47 47 or get your niece to visit the local Citizens' Advice Bureau or law centre