Everybody is aware that there is an obligation of saving others. It is also clear that one needs to exert effort and even expend money to save others. You are even allowed to speak lashon harah to save another's life. The question is a person required to suffer embarrassment and degradation to save another person's life? Rav Moshe Feinstein says yes.
Vayikra (19:16) states, “You shall not go around spreading gossip amongst your people nor shall you stand idly by the blood of your fellow man – I am the L‑rd.”
This is codified in Shulchan Aruch(C.M. 426:1): If you see someone drowning in the sea or being attacked by bandits or wild animals and it is possible to save him by yourself or to pay others to save him and yet you don’t save him or alternatively you hear non‑Jews or informers plotting to do him harm and yet you don’t inform him or alternatively you know that non‑Jews or bandits are planning to attack him and you are able dissuade them and yet you don’t or other such scenarios – you are violating “do not stand idly by the blood of your fellow (Vayikra 19:16).
Chinuch( #237) adds This means not only are obligated to try and save his life yourself but you need to also take the trouble and hire others if that is what is needed. The basis of this mitzva is well known because if you try and save others then others will try and save you. This is the basis of civilization and G‑d desires that society be preserved.
However Sanhedrin (73a) notes that there are in fact two verses - the verse in Vayikra and the verse to return lost objects and saving a person is a type of returning a lost object. Whence do we know that if a man sees his neighbor drowning, mauled by beasts, or attacked by robbers, he is bound to save him? From the verse, Thou shalt not stand by the blood of thy neighbor.’ But is it derived from this verse? Is it not rather from elsewhere? Viz., Whence do we know [that one must save his neighbor from] the loss of himself? From the verse, And thou shalt restore him to himself!9 — From that verse I might think that it is only a personal obligation,10 but that he is not bound to take the trouble of hiring men [if he cannot deliver him himself]: therefore, this verse teaches that he must.
Rav Shlomo Kluger therefore learns from this gemora that in fact that the same parameters for returning lost objects applies to saving lives. In particular that just as in returning lost objects one does not need to embarrass and degrade himself (if it is not in accord with his dignity)- he doesn't have to cause himself embarrassment - even to save a life.
This conclusion is strongly rejected by Rav Moshe Feinstein (Y.D. 2:174.3) [bottom of first colum] in his discussion of saving a person who attempted suicide.