So if a user is logged into your site and they have items in their cart but do not buy the items. It would be a nice feature if the system sent the user an email saying they have not completed their order. Newegg uses this feature and I think it offers a nice opportunity for a second chance at the sale.
You might want to add your comments to the following feature request:
This feature is currently scheduled for inclusion in v2.1. You can vote for this feature in the Ideas forum:
You can review the specification for this feature in this Roadmap thread: