Can fat transferred sink?

I'm gonna get fat transferred to my cheeks to correct a previous buccal fat removal. I know I can't predict how much fat will stay but this is not my biggest worry. I wonder if the fat from the fat transfer can "sink" (migrate) and end up in my lower face. I'm also afraid of looking unnatural or ending up with saggy skin. Are these possibilities? My doctor will be very conservative and only inject around 4cc in each cheek. I'm willing to go through a second procedure if needed. Thank you

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