Nedarim 40A

רב חלבו באיש. לא איכא דקא אתי. אמר להו: לא כך היה מעשה בתלמיד אחד מתלמידי רבי עקיבא שחלה. לא נכנסו חכמים לבקרו, ונכנס רבי עקיבא לבקרו, ובשביל שכיבדו וריבצו לפניו, חיה. אמר לו: רבי, החייתני. יצא רבי עקיבא ודרש: כל מי שאין מבקר חולים כאילו שופך דמים.

Rav Ḥelbo fell ill. There was no one who came to visit him. Rav Kahana said to the rabbis: Didn’t the incident involving one of the students of R' Akiva who became sick transpire in that manner? In that case, the rabbis did not enter to visit him, and R' Akiva entered to visit him and instructed his students to care for him. And since they swept and sprinkled water on the dirt floor before the sick student, he recovered. The student said to R' Akiva: my teacher! you revived me. R' Akiva went out and taught: With regard to anyone who does not visit the ill, it is as though he is spilling blood, as it could be that the sick person has no one to care for him. If there are no visitors, no one will know his situation and therefore no one will come to his aid.

כי אתא רב דימי, אמר: כל המבקר את החולה גורם לו שיחיה, וכל שאינו מבקר את החולה גורם לו שימות. מאי גרמא? אילימא כל המבקר את החולה מבקש עליו רחמים שיחיה, וכל שאין מבקר את החולה מבקש עליו רחמים שימות. שימות סלקא דעתך?! אלא: כל שאין מבקר חולה, אין מבקש עליו רחמים, לא שיחיה ולא שימות.

When Rav Dimi came from Eretz Yisrael to Babylonia he said: Anyone who visits the ill causes that he will live, and anyone who does not visit the ill causes that he will die. The Talmud asks: In what way are his actions the cause of that result? If we say that anyone who visits the ill pleads for mercy from God that he will live, and anyone who does not visit the ill pleads for mercy that he will die, does it enter your mind that he would pray that the sick person will die? Rather, anyone who does not visit the ill does not plead for mercy for him, neither that he will live nor that he will die. Since he might have saved the sick person with prayers had he visited, his failure to visit is tantamount to causing his death.