When a person finds himself in a grave crisis, and his heart is about to shatter with grief and fear, at this point, he turns to Allaah with a heart like that of no other person. The quality of sincerity that he displays, and the desperate need that he feels for the Mercy of his Lord, is so strong and pure that it is a duaa that is answered in all situations, regardless even of, whether the person is a Muslim or not! Yes, even the duaa of the kaafir is sometimes accepted, and that is part of the perfection of Allaah's Lordship, for He is the Rabb of the Muslim and the Kaafir.
Allaah says: "Is He not (the One) who responds to the distressed one when he calls out to Him." (Q[Naml]: 62) So if Allaah responds to the disbeliever in this situation, then how about the sinful Muslims? And how about the sincere, pious believer, how can he give up hope of being answered?" AI-Qurtubi wrote: "Allaah has guaranteed the response to the duaa of the one in distress, as He Himself informed us of this (guarantee). And the reason for this is that the one in distress will turn to Him with a pure sincerity, cutting his hope off from all other sources. And sincerity to Him is the cause of (gaining) His protection, regardless of whether it emanates from kafir or Muslim, evil or pious!" (Al-Jami' li Ahkaam al-Qur'aan).
Also, the period after a calamity has befallen a Muslim presents an auspicious time for supplication. However, it is necessary that the person displays patience and satisfaction at Allaahs decree, and not wail or lament over misfortune. Umm Salamah (RA) narrated that the Prophet (sallallahu alayhi wa sallam) said: "There is no Muslim that is afllicted with a calamity, and he says what Allaah has commanded him to say: To Allaah we belong and to Him we will return! O Allaah! Give me the rewards (of being patient over) this calamity, and grant me the rewards better than it to replace it, except that Allaah will give him.something better to replace it. Umm Salamah (RA) said, "So when (my husband) Abu Salamah died, I said this duaa, but could not help thinking who is better than Abu Salamah (i.e. no one can replace Abu Salamah)! Then the Prophet (sallallaahu alayhi wa sallam) himself sent me a messenger proposing to me, so Allaah blessed me with someone better than Abu Salamah" (Muslim).