Is it permissible to send messages seeking relief and assistance from benefactors, or is this considered asking others for what they possess, which is religiously blameworthy? And what are the cases in which it is permissible to seek relief from rulers and people of virtue?

Allah praises the poor who maintain their dignity, and Islam condemns begging from people. Scholars have forbidden begging except out of necessity. Begging is permissible only for three types of individuals: one who is in extreme poverty, one who is burdened by an overwhelming debt, or one who has suffered a disaster. If you are wealthy or capable of earning a living, it is not permissible for you to beg from people. However, if you are in dire need, then it is permissible for you. Nevertheless, maintaining your dignity and refraining from asking people is better for you. Therefore, ask Allah for His bounty.