Is it permissible to supplicate for death due to the loss of virginity in an accident, and can the Hadith: "O Allah, grant me life as long as life is good for me, and cause me to die when death is good for me" be employed in this context?

There is no need for worry or fear. Place your trust in Allah and accept whoever proposes to you from among those who possess religion and good character. If the suitor asks you about the reason for the loss of your virginity, inform him that it was due to an accident. This is not something to be condemned, as virginity can be lost without intercourse. Wishing for death due to fear of exposure is not appropriate, for Anas reported that the Messenger of Allah (peace be upon him) said: “None of you should wish for death because of some harm that has befallen him. If he must wish, let him say: ‘O Allah, keep me alive as long as life is good for me, and cause me to die when death is good for me.’” (Agreed upon). Whoever trusts in Allah, He will suffice her in what concerns her. Allah Almighty says: "And whoever fears Allah - He will make for him a way out" and "And whoever relies upon Allah - then He is sufficient for him."