As Cokayne points out, abeyance is merely a modern rule that approximates medieval practice.
However, in applying the modern rule, both titles descend to heirs general, which left them in abeyance between the daughters of Sir Owen West, and this situation persists to the present day with their respective heirs.
In 1572 William West, the heir male and nephew of the co-heirs general, was created Baron De la Warr, but not Baron West, by letters patent.
Cokayne argues that there is no reason to assume that this changed the status of the title Baron West, but given the irregular practice used, it is just conceivable that a modern claimant to the Barony of West would be refused on the basis that the title was merged into the Barony of De la Warr, along with the estates.
Some genealogical sources claim that Sir Thomas West (1251–1344) of Hempston Cantilupe, in Devon, was summoned to Parliament and became Baron West in 1342, but this is not supported by Cokayne.