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By default, there are four statuses available: Open, In Progress, Done and Skipped. You can customize that on a dedicated page.
To see the statuses page navigate to Jira Settings > Apps > Statuses.
After the status is added the only editable property of it is color. In order to change other properties, it is necessary to delete the status and then add it again with changed properties.
All statuses except for Open and Done can be deleted. The reason for this is that these two statuses are default ones for unchecked (not finished) and checked (finished) items, respectively.
If the status used by a checklist item is deleted, the item will be displayed with either Open or Done status, depending on the "checked" property of the item.
To undo status deletion simply adds a new status with the same name.