This is an issue where stacked items in a shulker box will unstack and replace other items.
To reproduce:
Allow cakes (for example) to stack to 64 in both inventory and chests.
Place a stack of 64 cakes in the upper-left square of a shulker box.
Fill the other squares with any other items.
Break the shulker box.
Place and reopen the shulker box.
The cakes will have unstacked and replaced the items to the right of them.
Stackableitems version 1.0.9
Paper version 1.14.4

This is fixed as of v1.0.10

If you're still experiencing any issues after updating, please create a new ticket with as much information as you can.

Confirmed that it's shifting contents to the right. Just to confirm, are you wanting cakes to stack in shulker boxes in the first place?

Also, if you could jump on discord or provide your items.yml config, that would be helpful.

Yes, adding stacking support for shulker boxes is probably the best fix for this issue but it's not critical that shulker boxes allow stacking as long as they don't remove items like they do now.
items.zip

Can you try out the following dev build and let me know if it fixes your issues?

That appears to have fixed it. :)