What's your question? Ask

I can suggest a few things for you to look for -- damage on a main stem on the side near the fence could cause die back; someone spraying herbicide on the other property which could have blown over to your side; the plant may simply have run its course. This article may shed some light on the problem: https://www.gardeningknowhow.com/ornamental/shrubs/winter-daphne/care-for-winter-daphne.htm

Ordinary balanced fertilizer (e.g. 6-6-6 or 10-10-10) will be fine. But did you know that fertilizer is not always what potted plants need? Before you decide to fertilize, evaluate the soil (too wet, too dry, too old,) the light (not enough, too much,) the plant's history (new or old, recently moved, fertilized frequently or infrequently,) possibility of bugs or diseases. After you've eliminated the possibility that you need to change the watering, the light, repot, or treat bugs or disease, then you can think about fertilizer. One thing you should include in your evaluation is that daphne does not do well as a houseplant unless you have a solarium for it to live in. This article has more information on these plants: https://www.gardeningknowhow.com/ornamental/shrubs/winter-daphne/care-for-winter-daphne.htm

Yes, you can propagate from stem cuttings and make new plants from the broken one!

Here are some links to help you.

https://content.ces.ncsu.edu/plant-propagation-by-stem-cuttings-instructions-for-the-home-gardener/
https://www.gardeningknowhow.com/ornamental/shrubs/winter-daphne/care-for-winter-daphne.htm
https://www.gardeningknowhow.com/garden-how-to/propagation/cuttings/root-stimulating-hormone.htm

I would pot them individually and wait until they are at least 12" high to plant outdoors.

https://www.gardeningknowhow.com/ornamental/shrubs/winter-daphne/care-for-winter-daphne.htm

It sounds like a pest of some kind or even a fungus is attacking the shrub. I would try treating it with Neem oil spray, which will help with both insect pests and fungus. Here is more information: https://www.gardeningknowhow.com/problems/pests/neem-oil-uses.htm

You are not alone with issues with Daphne odora growing problems.
Known for their fussiness, the can be difficult to keep alive let along bloom again.
They have a stringy root system and can die from root rot easily.
They need very well draining, lime based soil.
Partial shaded location and a mound or hilled planting spot can help.
There is a variety 'Eternal Fragrance' that is know to be hardier.
If the plant does find a planting spot that it is happy with, it can live for years.
Do not over fertilize. To much nitrogen can cause lack of flowering.

https://www.gardeningknowhow.com/ornamental/shrubs/winter-daphne/care-for-winter-daphne.htm