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

Fat cells can't migrate.

However, if you ask the question "Can you gain volume in another area after liposuction, even if you don't gain any weight?", the answer is that it is possible. For most patients, this slight gain in volume in another area of the body will not be noticeable.

There have been studies looking at breast enlargement after liposuction of the abdomen (Plastic and Reconstructive Surgery, 2007 April 15;119(5):1584-9). They DID show that a certain number of women gained volume in their breasts (about 40%). I don't know of any studies looking at other areas of the body - ie thigh enlargement after lipo of the abdomen. So, if you are worried about volume gain in your breasts, you should ask your doctor at the consultation. I wouldn't worry about gaining volume in other areas.

Thank you for the question; it is a common one.
Liposuction surgery removes fat cells; the fat cells that are removed are permanently removed.  From this standpoint therefore, the results are permanent. However, if the patient gains weight the fat cells that remain in the area will grow.  Obviously, there may be relatively more fat cells present on other anatomic parts (these parts may grow relatively more when patients gain weight after the liposuction procedure).
I hope this helps.