That usually is a pollination problem, not much one can do except maybe pollinate flowers by hand. I can't tell where you are at? Look at my name and you can see I'm in zone 5b/6A in South East Michigan. Winter injury could be a cause too. I lost some canes, but I didn't experience incomplete fruit.

Here is a link that might be useful: pollination

I am in southwest PA - zone 5.
We did have a harsh winter so maybe covering the bush over the season would help?
I also have a small vegetable garden, and I've never had issues with those plants being pollinated.
Do you know if amount of sunlight plays a crucial role? A neighbor told me this but I wanted to verify that too much sun would cause incomplete fruit.
Thanks, Aimee

Usually too much sun causes white drupelets, not incomplete ones. My guess is bad pollination. Why? Maybe lack of insects, they do bloom early.
My raspberries are in full sun and I never seen sun damage. I do have a 2nd and 3rd patch not in full sun also. They do fine too.
If canes die before fruiting is complete, it is winter damage. We had a severe winter, hopefully that is over. You may not need to cover them. I didn't see this as a problem on my winter damaged canes, mostly they tried to fruit, did fruit about 50%, then the cane died. All fruits were full and good too! So I don't think it is winter damage. What you could do is add some flowers next year. Like Borage, man does that attract insects! My borage did bloom after the raspberries, but any early flower would be good.

Drew51, Thank you so much for your answer! It is truly helpful. I will try placing flowers around my berry bush next year to increase pollination.
It's been frustrating to collect berries in the local woods a few blocks away, while my berries are not usable.

Take Care, Aimee

I also forage berries. Even though my harvest is huge, you can never have too many.
I grow Allen, Jewell, and Niwot black raspberries.

Here's a link to beneficial flowers

Here is a link that might be useful: Flowers for Beneficial Insects