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.

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.

Waxleaf Privets do exceptionally well in a pot, if they are watered frequently---they do not need to be watered as much as say, a rosemary. They can be root bound and survive. They will grow in sun or shade. They can be easily shaped into very decorative spheres, boxes, poodles, small trees, etc. You will not have that many birds feeding on it's seeds (distributing them) if you keep it on a porch (and I have not seen any growing in the wild but then again, there is usually little ground water around here).

I've lost 3 more privet. They were here 45 years ago. I have to replace them, but I need an evergreen shrub that can be kept narrow, grows in shale, tolerates drought and cold winters (not so cold the past few years--climate change), and is not poisonous to birds. It might have to be yew. It's tough. The drupes have a stage when they are very sweet and edible--birds and squirrels love them. They can be brutally pruned and come right back. I have yews that were here when we moved in. We have dug them up and transplanted them many times. I keep one trimmed in a 5 ft dome to keep it dense. This year blue jays nested there. My neighbor has junipers overhanging our garden where a catbird nests every year. One nested in the weigela (not native, but loved by bees and hummingbirds). We put a nest box high in the arbor vitae and wrens nest there regularly. A cardinal nests nearby but I haven't found the nest. When the privet was dense cardinals nested there. I'm in a town in an area overflowing with people and houses. This year we hosted painted lady butterflies, monarchs, viceroys, admirals, sulfurs, skippers, and small blue ones whose name I forget, along with the cabbage whites. My privet hides fledglings and adults, too, when they see a hawk. My lot is only 50'x100' and the house takes up the most room; an embankment limits our front garden but. it's loaded with life. The privet doesn't spread elsewhere. I live across the street from a river park. A privet has never shown up anywhere. Plants aren't good or bad. They just need to grow where they are wanted and leave other people's gardens alone. Love that privet.