Degenerate dimensions commonly occur when the fact table's grain is a single transaction (or transaction line). Transaction control header numbers assigned by the operational business process are typically degenerate dimensions, such as order, ticket, credit card transaction, or check numbers. These degenerate dimensions are natural keys of the "parents" of the line items.
Even though there is no corresponding dimension table of attributes, degenerate dimensions can be quite useful for grouping together related fact tables rows. For example, retail point-of-sale transaction numbers tie all the individual items purchased together into a single market basket. In health care, degenerate dimensions can group the claims items related to a single hospital stay or episode of care.