Although the LHC experiments have searched for and excluded many proposed new particles
up to masses close to 1 TeV, there are many scenarios that are difficult to address at a
hadron collider. This talk will review a number of these scenarios and present the
expectations for searches at an electron-positron collider such as the International Linear
Collider. The cases discussed include the light Higgsino, the \stau~ slepton in the coannihilation
region relevant to dark matter, as well as other BSM signatures.The studies are based on the ILD concept at the ILC.