Hungary's Panna Udvardy says she was sent "disturbing" messages including a picture of a gun, warning her family would be harmed unless she lost a tennis match.
Jack Draper says he no longer has "any fear" around the arm injury that plagued him for eight months as he prepares to begin his Indian Wells title defence.
Players have criticised the decision for a tennis tournament to be held in the UAE in the midst of Iranian attacks - including one still stranded there.