The hedge is not dying. It is a result of the pruning. If you were to peek inside a thick hedge you will find the center is only filled with branches and the leaves are only on the outside where there is light to reach them. I can recover but it will be unsightly for a long time especially if it is a slow growing species. Hedges should be pruned so that they are in a wedge shape with the bottom being slightly wider than the top. Most people prune the other way with the top wider and end up with bare legs on the bottom of the hedge. If it is an older hedge you cannot drastically reduce it or you get what happened after you pruned your hedge. Once the hedge is shaped, you prune only to maintain that shape and only the outer leaves.
https://ag.arizona.edu/pubs/garden/mg/p ... edges.html
There is a season for pruning hedges and depending on what the hedge is composed of pruning may be necessary anywhere from twice a year to every month. I have a rhapsiolepsis indica (Indian Hawthorne) I usually only prune it twice a year and only to keep it in shape. It has grown about 5 inches from the time I bought the house in 1989. I did have to take out some large branches on one side because it had grown out about a foot and was getting too close to the driveway. When I took it out, I had a gaping hole on the side, pretty much how yours looks. It has taken about 5 years, but it is filling back in again. Indian Hawthorne is a very slow growing plant. Boxwood grows faster so it may not take as long to fill in, but it will look bad for awhile.
You could have a good landscaper come in and trim it down to the base. It is sometimes better to let it start over, but it will take years to fix it. If it is in good condition, with feeding and care it will come back. If it is very old, you might want to start new, but have it properly shaped and maintained.
Happy gardening in Hawaii. Gardens are where people grow.