Content of Unlimited Text Field not saved

Problem/Motivation

There are two issues (could be the same one):
* Field Content disappears when clicking "Add another item" in a unlimited field text.
* Field Content disappears when saving the node (clicking "Save and publish" button

No browser console log errors.

Steps to reproduce:
Edit the built-in "article" content type
Add a new field of type "Text (formatted)"
Choose "Unlimited" for the number of values
Create an article
Fill the new Text Field
click "Add another item" and all the multiple Text fields will get empty.
Fill anyway both fields.
Save the node.
The content is not displayed.
Edit the node... all the multiple text fields are empty.

Proposed resolution

Find the bug. Test other types of unlimited fields.

Remaining tasks

User interface changes

API changes