Answer:
1. I am out of sugar because, Ms. Smith, who lives next door, had come to borrow it.
2. As it began to rain, they went inside.
Step-by-step explanation:
Clauses often begin with adverbs like after, as, because, since, if, until, and when, went, begin.
It tells us of the time it began raining and hence changes a verb. A comma should immediately follow this.