This all depends on what filler is used. The vast majority of fillers used are made of something called hyaluronic acid (HA). Juvederm and Restylane are the two most common brands of HA. These products will dissolve in time and will not lead to jowling or sagging. HA doesn't migrate, you can "push out" the edges with massage early on, but it won't altogether move to a different location. HA fillers can be dissolved on purpose when using a product to dissolved it (hyluronidase). The dissolving is very quick in this case taking only hours. Otherwise, HA fillers last from weeks to a few years depending on the location, the patient's genetics, and filler brand chosen. Other fillers are permanent and, in my opinion, should be avoided. Silicone is an example. It is legal in the US because of its usefulness in treating detached retinas. People (doctor and other) use silicone "off-label" for cosmetic injections despite a history of complications and FDA warnings against its use in that manner. My recommendation is to stick with using HA fillers and a doctor who is talented at injecting them. HA fillers produce tremendous results for quite a number of problems. A reputable injector will know what sort of results you can expect with your specific concerns. The key is to select your battles, some problems can be treated with great success, others not so much. An honest injector will steer you away from treatments that are not likely to succeed so you can focus your efforts on successful treatments.