In ArcGIS Pro, when checking the Allow Nulls check box on a feature class with features the returned error message, "Error 001625: Failed to alter field is nullable" does not give a meaningful description of the issue.

Workaround

Workaround identified from case #0328049 by Sahil Purohit:

Step to be executed from the RDBMS application:

1. Execute the below-mentioned SQL query to alter the table and the column to allow null values: 

ALTER TABLE table_name ALTER COLUMN column_name data_type [(Column_Size)] NULL;

Steps to be executed from the ArcGIS Pro application:

1. Load the respective feature class in the table of contents in ArcGIS Pro.
2. Right-click on the feature layer -> data design -> fields.
3. Check the box "Allow Nulls" on the respective field and click Save.

Steps to Reproduce