In previous NX releases (eg NX12) the user would receive a warning notification stating "Deleting or editing these objects will affect other features or constraints in sketches", but in NX2007 they no longer see the warning.
SolutionA synch problem between the Customer Defaults and the Modeling Preferences was reported as PR10285685. Customers should be able to fix that by manually enabling your Preferences-> Modeling-> Edit-> "Notify on Delete if Feature has Dependent" switch
This issue is corrected in NX2206.