We learned how to express feasibility in the section on the potential form quite a while ways back. In this section, we'll learn some advanced and specialized ways to express certain types of feasibility or the lack thereof. Like much of the grammar in the Advanced Section, the grammar covered here is mostly used for written works and rarely used in regular speech.
This grammar is used when there's something that just can't be helped and must be done. It is the negative version of the grammar we previously covered for something that has to be done. It uses the negative of the verb 「得る」 or "obtain", to roughly mean that "one cannot obtain not doing of an action". This means that you can't not do something even if you wanted to. As a result of the use of double negatives, this grammar carries a slight suggestion that you really don't want to do it, but you have to because it can't be helped. Really, the negative connotation is the only difference between this grammar and the grammar we covered in this "have to" section. That, and the fact that this grammar is fancier and more advanced.
This grammar uses an archaic negative form of verbs that ends in 「～ざる」. It is really not used in modern Japanese with the exception of this grammar and some expressions such as 「意図せざる」. The rules for conjugation are the same as the negative verbs, except this grammar attaches 「ざる」 instead. To reiterate, all you have to do is conjugate the verb to the negative form and then replace the 「ない」 with 「ざる」. The two exception verbs are 「する」 which becomes 「せざる」 and 「くる」 which becomes 「こざる」. Finally, all that's left to be done is to attach 「を得ない」 to the verb. It is also not uncommon to use hiragana instead of the kanji.
This grammar is very similar to the one we just learned above except that it uses the verb 「止む」 to say that one cannot obtain the stopping of something. Remember that we normally can't just attach the 「を」 direct object particle to verbs, so this is really a set expression. Just like the previous grammar we learned, it is used to describe something that one is forced to do due to some circumstances. The difference here is that this is a complete phrase, which can be used for a general situation that doesn't involve any specific action. In other words, you're not actually forced to do something; rather it describes a situation that cannot be helped. If you have already learned 「仕方がない」 or 「しょうがない」, this grammar means pretty much the same thing. The difference lies in whether you want to say, "Looks like we're stuck" vs "Due to circumstances beyond our control..."
Since this is a set expression, there are really no grammar points to discuss. You only need to take the phrase and use it as you would any regular subordinate clause.
The meaning and usage of 「かねる」 is covered pretty well in this jeKai entry with plenty of examples. While much of this is a repetition of what's written there, 「かねる」 is a ru-verb that is used as a suffix to other verbs to express the fact that something is impossible. By impossible, we are not talking so much about physical impossibility, such as creating matter out of nothing, but more about what cannot be accomplished given certain conditions.
「かねる」 is more often used in the negative as 「かねない」 to indicate that there is a possibility that the verb in question might happen. As the jeKai entry mentions, this is usually in reference to something bad, which you might express in English as, "there is a risk that..." or "there is a fear that..."
One important thing that the jeKai doesn't mention is how you would go about using this grammar. It's not difficult and you may have already guessed from the example sentences that all you need to do is just attach 「かねる」 or 「かねない」 to the stem of the verb.