I grew up in a house that had asbestos and I'm still very healthy today years later.
Asbestos really only becomes a problem and a mesothelioma cancer causing product when it becomes airborne by being disturbed and breathed in.
Still it usually takes years of exposure of the asbestos particles to be affected by it and to contract mesothelioma.
My parents also grew up and lived in houses with mesothelioma causing asbestos and are still healthy and alive today.
It's usually people working in factories making things with asbestos or construction workers who worked with asbestos years ago who eventually get the mesothelioma from the asbestos.
So as long as you don't disturb the asbestos material and cause it to become airborne then you'll be safe living in the house with asbestos.
If you want it removed then you should hire a professional to remove the asbestos to prevent any health problems of doing it yourself.