Privets are very resilient. If it is Privet (I can't quite tell, and I'm no plant expert), you can hack it way down and it will bounce right back. But you should probably wait until late winter/early spring. Someone else can confirm, but I don't think this is the time of year for heavy pruning for this sort of thing. If it makes you feel more confident about it... Earlier this year (Feb/March) I cut my Privets WAY back. I'm talking like 20' tall bushes/trees (they were very overgrown) that we hacked back to about 4-5' of mostly just trunks/branches. They have already grown back to looking normal and bushy again. I was afraid I might kill them by cutting them back too far, but in fact I think they need to be cut down even lower next year.

Privets are pretty tough cookies, and even if you sheared them to the ground, they would probably start sending more shoots up. They also grow fairly fast. Since you are not growing them for their flowers, you can prune in June, and again in late August. Twice a year should do it. When you achieve the desired height and width, just keep pruning to that shape. Basically, the more you prune, the denser the hedge will get. If you want to get some more Privets going for the ones which died, just propagate a stem cutting. They will root easily in a pot in one season - maybe less - and you'll be able to fill-in those gaps. Nicole.

I took a look at your pics and it doesn't look "dead" or on death's door to me. It looks to be in pretty good shape, some branches (especially if they are on the inside) are bound to die because they get less light or air. Take your finger nail and scrape a little of the trunk and branches very lightly. If you see green underneath then the tree is alive if you see brown then it is dead. I wouldn't prune or repot until spring comes around and you see that new growth is appearing and the plant is starting it's growing cycle.

Sorry for the necro-post, but I came across this thread as I was Googling for something else. I just wanted to chime in with my observations... I work with a tree guy and these Ligustrums are one of our top three removal trees. Hackberry and red cedar are the others. The main reason for removal is because they get way, way too large for the area in which they are planted. Other major reasons are a desire to 'go native' and the mess that they leave with the berries. The boss can't stand these things, and he's one who will go to great lengths to save an otherwise-healthy tree... even a hackberry. People call hacks 'trash trees' and while they do have some bad habits, are weak, and are not very long-lived trees compared to other species-- they do provide good homes for wild birds, butterflies (hackberry emperors and tawny emperors especially) and other critters. Even for all of the negatives that we commonly associate with hacks, he would rather save a hackberry over a ligustrum.