Gemara

(Beraisa): If Reuven sees Shimon drowning in a river, or being dragged by an animal, or being Nirdaf (pursued) by bandits, he must save him - "Lo Sa'amod Al Dam Re'echa".

Question (Beraisa) If one is in danger of dying, others must save him. We learn from "va'Hashevoso Lo."

Answer: From there, one might have thought that the onlooker must exert himself to save him, we would not know that (if he cannot) he must hire others to save him. "Lo Sa'amod Al Dam Re'echa" teaches that he must hire others.

74a (Rava): If Levi was Rodef David, who was Rodef to kill Ploni, and Levi broke Kelim, whether they belong to Ploni or to others, he is exempt. Letter of the law, he is liable. This is an enactment, lest people refrain from trying to save a Nirdaf.

Kidushin 8b - Question (Rav Mari): If a dog was chasing Leah, and David said 'be Mekudeshes to me with a loaf, and she said 'give it to the dog', what is the law?

With the Hana'ah that she is being saved, she is Makneh herself (to him).

Or, can she say 'the Torah obligated you to save me!'

This question is unresolved.

(Beraisa): If one said 'be Mekudeshes to me with a loaf', and she said 'give it to this Oni', she is not Mekudeshes, even if the Oni relied on her for his food.

This is because she can say 'also you must feed Aniyim.'

Rishonim

Rambam (Hilchos Rotze'ach 1:14): Anyone who could save a Nirdaf, but does not, transgresses "Lo Sa'amod Al Dam Re'echa." The same applies if Reuven sees Shimon drowning, or bandits are pursuing him, or a vicious animal is coming upon him, and Reuven himself could have saved him or hired others to save him, but he did not. The same applies if he heard Nochrim or informers plotting evil against him or setting a trap against him, and he did not tell Shimon, or he knows that a Nochri or Anas is coming against and he can dissuade him, but he did not.

Rosh (Sanhedrin 8:2): The Nirdaf must pay the expenses of the one who saved him. David need not save Ploni with David's money if Ploni has money. If Levi was Rodef Ploni and Ploni broke someone else's Kelim, he is liable. If David were obligated to save Ploni with David's money, Ploni would be exempt!

Question: A Hekesh from Rotze'ach to Na'arah Me'orasah teaches that there is a Mitzvah to kill a Rodef. Why is another verse needed to obligate saving someone drowning or in other mortal dangers?

Answer #1 (Tosfos 73a DH Lehatzilo): The Hekesh teaches that there is an Aseh to save. "Lo Sa'amod Al Dam Re'echa" is a Lav to neglect saving.

Answer #2 (Chidushei ha'Ran 73a DH v'Chi): The Mitzvah to kill a Rodef is when it is totally clear that he wants to kill. One is obligated to save someone even from Safek mortal danger.

Ritva (Kidushin 8b DH Kelev): Perhaps the girl being chased by the dog can say 'the Torah obligated you to save me', i.e. on condition to be paid back. Only when one volunteers to save without the other's Da'as, he is not paid. Here, she asked him to give it to the dog. Redeeming captives is not called Mavri'ach Ari (who is not paid for saving another's property) because the damage already came.

Me'iri (Kidushin 8b): "Lo Sa'amod Al Dam Re'echa" applies only when the victim agrees to pay back the one who saves him. If not, he need not save, for one may not save himself with another's money. Some say that even though one may not save himself with another's money, one who could save must do so, even if he cannot get back his money in Beis Din. A verse was needed to exempt from unloading if the owner does not help. If not, the onlooker would need to unload by himself! Even if you would say that he is exempt even without a verse, perhaps that is only because the owner could help but refuses. Also, saving lives is more stringent.

Magi'ah (4): Women do not know all laws. Perhaps she knows that the Mekadesh must give Tzedakah, just like her, but not that he must save her!

Kovetz Shi'urim (76): Rashi explains that the question is whether saving her is considered Hana'ah, since he is obligated to save her. One may give the half-Shekel (that everyone must give to Hekdesh each year) for one Mudar Hana'ah from him. It is not considered Hana'ah from the giver, rather, from the Mitzvah (Shitah Mekubetzes Kesuvos 108). According to Rashi, perhaps the question could be whether she must pay, since he needed to save her. However, a divorced mother obligated to nurse her baby due to danger is paid (Kesuvos 59)! Perhaps Rashi agrees that we ask only about her intent.

Gilyonei ha'Shas (Kidushin 8b): Even though she must pay him, since he must give the loaf itself to the dog to save her, this is like Kidushin with a loan, so she is not Mekudeshes. However, if wages are due only at the end, what he gives to her at the end l'Shem Kidushin is like giving money (48b). Even though he needed to return the rings to her, since he pardons what she owed at that time, she is Mekudeshes. The same applies here.

Poskim

Shulchan Aruch (CM 426:1): If Reuven sees Shimon drowning in a river, or bandits are pursuing him, or a vicious animal is coming upon him, and Reuven himself could have saved him or hired others to save him, but he did not, he transgressed "Lo Sa'amod Al Dam Re'echa." The same applies if he heard Nochrim or informers plotting evil against him or setting a trap against him, and he did not tell Shimon, or he knows that a Nochri or Anas is coming against and he can appease and dissuade him, but he did not.

Gra (1): The Gemara discussed a vicious animal dragging Shimon. The same applies if it is chasing him, like we find in Kidushin 8b.

Question (SMA 1): The Tur brings the Rosh, who proved that if Shimon has money to save himself, he must pay Reuven's expenses. Why did the Shulchan Aruch and Rema omit this?

Shach (1): The Rema brings it in YD 252.

Rema (YD 252:12): If Reuven redeemed Shimon from captivity, Shimon must pay him, if he can. We do not say that Reuven was Mavri'ach Ari.

Yam Shel Shlomo (Bava Kama 6): If Shimon was held for a monetary claim against him, Shimon need not pay more than his value, even if Reuven paid more. He can say 'I did not want to be redeemed for so much.' However, if he was taken for Nefashos, he was obligated to redeem himself for any amount of money, so he must pay whatever Reuven paid.

Chasam Sofer: Shimon must pay only if he had money when Reuven redeemed him. If he was an Oni at the time, he is exempt even if he became rich later, like we say about Tzedakah (253:4).

Rema: Shimon must pay immediately. He cannot say 'we will go to Din, and I will follow the ruling.' If later Shimon has a claim against Reuven, he wil take him to Din. If not (that Shimon must pay immediately), no one would redeem another.

Shach (13): Even if Reuven redeemed orphans, they must pay immediately. Normally, we wait for orphans to mature, in order to receive testimony against them. Here we need no testimony. The Torah obligates saving them! Also, one would not save orphans if he would not be paid until they mature (Mahariyo Sof 148).