The structure of the period (and as a consequence the placement of the verbs) is dictated in German by the breakdown of said period in main clause versus subordinate clause; moreover, according to the type of subordinate clause we are dealing with, the position of the verb in said subordinate clause may vary. Furthermore notice that it is such subdivision in main + subordinate that rules the positioning of the comma, but the comma itself does by no means dictate the position of the verb in the subordinate clause.
Main clauses
In the main clause the verb always goes to second position, the first position being anything (also itself a subordinate clause).
Ich spiele Fußball, wenn ich glücklich bin
position one (P1) being the subject ich. But you could also say
wenn ich glücklich bin, spiele ich Fußball
P1 being the whole subordinate clause "wenn ich glücklich bin".
Subordinate clauses
The general rule (though with exceptions) is that in subordinate clauses the verb is placed at the end. Before a subordinate clause one generally places a comma, therefore the common structure would be
main clause with verb in P2 + comma -->, + proposition introducing the sub clause + clause + verb
In your examples:
Es gibt keine Möglichkeit, sein Leben zu retten
Er hofft, wo es keine Hoffnung mehr gibt
we follow exactly the aforementioned structure, hence they are correct according to the rules.
there isn't any Modal Verb at the second position (after the comma) to push the Second Verb to be at the end of the sentence.
Modal verbs are only one of the constructs where the accompanying verb must be placed eventually, but there are many others, in particular - as we are showing here - for subordinate clauses this is (almost) always the case. The absence of modal verbs doesn't therefore per sé exclude that a verb must be placed at the end.
Based on my limited knowledge, I assume the 2 sentences after the 2 commas should be: "... , sein Leben retten zu."
this can never be the case, why would you place zu after retten? Zu retten is the infinitive form of the verb retten, and "sein Leben zu retten" is a Konsekutivnebensatz, the rules explicitly stating that in such cases the verb (in its infinitive form) goes in last position keeping such infinitive form.
wo gibt es keine Hoffnung mehr.
This could be the case if the above sentence were a main clause; it being a subordinate clause the verb goes in last position, hence "wo es keine Hoffnung mehr gibt".
Ich mag Geschichte, deshalb lese ich ein Buch.
That's because the words deshalb/dann/daher/deswegen introduces another main clause by definition (see here).
Generality
We have stated that in subordinate clauses the verb must be placed at the end. This is true except whenever said subordinate clause in introduced by specific prepositions which, as exceptions, require the verb in the second position. These are exceptional prepositions/adverbs and must be learnt by heart (any attempt to classify them as sub-rules of sub-rules leads only to mental gymnastic whereby one could state the rule being A and the exception being B or completely viceversa, according to where we start). The classic case is "weil vs denn", both of which introduce causal subordinate clauses, with "denn" by definition turning the subordinate clause into the grammar rule of a main clause (see here).