Necrosis from Dermal Fillers in Tear Troughs?

The tear trough has vessels which can be injured with injection with fillers. Blunt cannulas don't have a sharp end to them so its very difficult to enter a vessel, particularly with cannulas that are 27g or larger. Eye injury would be the risk in this area so you need to go to a qualified physician for this injection. Most of the problems I read on realself are related to poorly performed tear trough injections.  Necrosis happens when filler either enters a vessel or compresses it. Yes, the glabella, nose, and piriform aperature are the most common areas but it can happen anywhere, including lips.  An experienced physician can also recognize these problem early and avoid any long term issues most of the time. 

I would recommend you start with a consultation (or a few) with board-certified injectors in your area. When I have seen necrosis, it has been near or in the lips, though yes, technically, it can occur in other places. The veins that run under the eyes are smaller and different than an arterial vein, which is what is usually blocked when there is necrosis. Around the eyes more common would be a hematoma than necrosis, though this is also still very rare.

If you seek injections from a qualified physician, you will already be limiting the risks. Plus, on the very small chance there is a problem, a physician can actually prescribe you meds and take care of a situation. Where a medspa or other aesthetic injector, cannot necessarily be as helpful. Remember that the experience of your injector is key in limiting risks. Yes, this is a cosmetic procedure, and yes, there are inherent risks, but many of those are limited based on the person you see as your injector.

"This answer has been solicited without seeing this patient and cannot be held as true medical advice, but only opinion. Seek in-person treatment with a trained medical professional for appropriate care."