The truck broke down, and the family walked ten miles because no one passed by who could rescue them.
the phrase "the truck broke down." and "family walked ten miles are considered the independent clause because they can't stand on their own. just by reading that phrase a person would realize he is keep hanging.
while the sentence/ phrase "no one passed by who could rescue them."
this is the subordinate clause also known as the dependent clause. this alone can be considered a sentence and can support itself.
hope this answered your question