Is It True That Fat Cells Will Migrate to Other Parts of Body After Lipo Even if the Person Does Not Gain Any Weight?

     Liposuction in one area depletes fat cells in that area.  As a result, if a patient gains weight the fat will be stored in other areas of the body preferentially. 

I do not believe that fat will migrate to other areas of the body if you don't gain weight, and I have not seen it do so after having performed liposuction for decades. However, with increasing age and hormonal changes, fat does redistribute whether or not you have had a liposuction. 

The best plant is to have a lipo, if you want and need one, and stay in good health, by eating healthfully and exercising. Also make an attempt to maintain normal hormone levels (bioidentical hormones) for someone about 35 years old. This will help you maintain muscle size, which burns calories even when you are asleep. Bone mass will also be preserved. 

We can't stop the aging process, but we can make every effort to slow it down, and that will help prevent excess accumulation of fat.

The situation you are describing is not true.  Liposuction permanently removes fat from the areas that are treated.  If you do not gain weight, you will not see an increase in fat elsewhere.  This is not a lost cause and if you have a problem area or two that you just can't seem to get rid of, liposuction is a great tool for improving your figure.  Good luck.