When you delete a record, it will be placed in a recycle bin, and it is no longer part of your database. All pedigree, mating, cage, and any other data will not longer be available. However, the animal name remains as "used" in the database.
When you purge a record, it is permanently removed and cannot be undeleted. The animal name will also become available.
To keep records as inactive, use sacrifice, discard, completed, etc. instead.
You can undelete any records form the deleted records list, as long as it is not purged.
If there are items in your recycle bin, you will see a Browse Deleted Link. Click on the link, and select items to undelete.
You can also permanently delete items in the recycle bin with the Purge Button.
