There are various thoughts on that subject. One is to increase the consumed fat so the body becomes more dependent on fat burning and that will induce the body to burn more body fat. The other is to reduce intake of fat so body will consume the stored groceries body fat. I have heard success stories from both methods that seems probably dependent on the individual. One thought is to bump up the fat consumption significantly for a period of time (actually increasing calories significantly) then as the body becomes better fat adapted and used to burning fat back off the consumed fat and the body will reach into its stores thereby burning the unwanted body fat.

Is any of the above true? Danged if I know. I personally never had a problem dropping the body fat as long as I kept insulin levels low (cut out nearly all of the carbohydrates that raise insulin levels). Now my wife on the other hand only lost about half the total weight she wanted to and has been stalled at that weight for probably five years now. But I will say when she goes out with her girlfriends she does not always eat according to plan so she may not always get her insulin levels down. Eating at home no problem (we just don't keep stuff or cook with stuff that raises insulin significantly). One problem my wife has though concerning high fat is she has no gallbladder and if she eats too much fat at once it goes right through her (no bolus of bile from the gallbladder to aid in the fat digestion). So she has not been able to try a very high fat diet. No problem for me. I tried a "fat fast" one day eating only butter for 24 hours and felt great. She would not be able to do that.

Kelly Hogan (My Zero Carb life) on Youtube has done a bunch of personal experiments with different levels of fat. Might do a Youtube search for her stuff.
https://www.youtube.com/results?search_query=myzerocarblife+kelly+hogan+high+fat #mce_temp_url#      

I have never counted how much fat I eat. But I will say if our meal is too lean I will be hunting for some fat later as a snack. Pork rinds of something like that. So for me fat definitely curbs my apatite and if I don't get enough will become hungry again.