|1.||Berti asked Ernie to lend himi some money.|
|2.||Johni and Maryj stayed until shej had finished checking the book for himi.|
|3.||Joani complained to heri parentsj that theyj never let heri go out on heri own.|
|4.||Spikei promised John that hei would finish the job.|
|5.||Spike persuaded Johni that hei should finish the job.|
In 1, there are two possible antecedents (Bert and Ernie) for him, but only the first of these makes sense.
In 2, there is only one male and one female, and so the antecedents for she and him are obvious. Though it would be possible that she and him refer to completely different people to those just mentioned in the sentence, this would not be our first interpretation (in the absence of further information).
In 3, there is again no ambiguity over who the anaphors her and they refer to, since there is only one singular female (Joan) and only one plural (parents).
In 4 and 5, it is possible that he doesn't refer back to the name indicated, but to the other one. But our most likely interpretations are the ones given, because of our understanding of what promise and persuade mean, as well as of the difference between would and should.