Can you afford to give up work? Carers' Allowance is pitiful
What are the health problems of the relative?
What is your relationship like with the relative? Are you close enough to give intimate care?
Will you get support from other relatives?
It is is different kettle of fish caring for somebody with a physical disability to looking after somebody with dementia.
I haven't given up a job to do it but have done it and have been involved professionally with many many carers. No two circumstances are the same but I think that the first thing to think about is whether its a practical possibility at all.
Can you afford it? how will it affect your return to the job market in the future? Will the care that you can give be enough? How long will it be enough for? Is it actually something that you will be able to do? Not everyone can.