A Product Backlog item is a description of a feature or functionality that adds value to the product. It is selected by the Scrum Team during the Sprint Planning, based on the Product Owner’s proposal and the Developers’ forecast. It is expected that the Product Backlog item will be completed by the end of the Sprint, meaning that it meets the Definition of Done, which is a formal description of the state of the Increment when it meets the quality standards required for the product.

However, if a Product Backlog item is not completed by the end of the Sprint, meaning that it does not meet the Definition of Done, then:

The item is not included in the Increment for this Sprint (B), which is a valid option as it ensures that only “Done” work is delivered to the customer and stakeholders. The Increment is a concrete and usable outcome of a Sprint that provides value and feedback. It should not contain any undone or partially done work that may compromise its quality, usability, or value.

It is put on the Product Backlog for the Product Owner to decide what to do with it (D), which is another valid option as it respects the authority and accountability of the Product Owner to manage the Product Backlog, which is an ordered list of what is needed in the product. The Product Owner can decide whether to re-prioritize, re-estimate, refine, or remove the incomplete Product Backlog item based on new insights and stakeholder needs.

The other options are not correct because they:

Review the item, add the done part of the estimate to the velocity and create a Story for the remaining work (A), which is not a good option as it violates the principle of commitment and transparency that underlies the Definition of Done. The Scrum Team should not count or report any work that is not “Done” as part of their progress or performance. The Scrum Team should also not split or create new Product Backlog items during or after the Sprint, as this may affect their alignment and focus on the Sprint Goal.

Only the stakeholders decide over acceptance of undone work and whether to release it ©, which is not a good option as it violates the role and responsibility of the Product Owner and the Developers to deliver a potentially releasable Increment at the end of each Sprint. The stakeholders can provide feedback and suggestions for the product, but they cannot accept or release any work that does not meet the Definition of Done.

References: : [Scrum Guide], The Product Backlog : [Scrum Guide], The Definition of Done : [Scrum Guide], The Increment : [Scrum Guide], The Sprint Planning : [Scrum Guide], The Product Owner : [Scrum Guide], The Developers