Hi Julien,
You may apply to sponsor a relative from overseas under the subclass 116 carer visa. It is a permanent visa and allows the relative to remain in Australia indefinitely.
There are three main parts to the carer visa:
1. Australian person has a medical condition which causes impairment - this involves a medical assessment by Bupa Visa Medical Services;
2. There is no other relative or community services who are able to provide the required care for the person - this is difficult and involves proving that other Australian family members or hospital/welfare/nursing services have been researched and are not available; and
3. There is a visa applicant who is willing and able to provide the required care - this invokes an assessment of their capacity, age, health, qualifications, family obligations etc.
The current processing times are very, very long - if you applied now, you could wait around 4-6 years for a visa. It is not an easy visa to get - the documents required are extensive - and I recommend seeking advice from an immigration lawyer.
Hope this helps.