Learn Italian: A forza di tirare, la corda ha ceduto. - From pulling so much, the rope gave way.

A forza di translates to "by dint of" or "from [doing something] so much." It introduces an implicit causal clause showing that a repeated or prolonged action caused the outcome. Yes, you can absolutely use a furia di instead; they are completely interchangeable here. Both are followed by the present infinitive (tirare).

Normally, implicit clauses with the infinitive require the same subject as the main clause. The rope isn't pulling itself, so why is this allowed?

Great catch! You're right that usually, the subject of the infinitive must match the subject of the main clause (la corda). However, a forza di and a furia di are often used with an unstated, general subject (like "someone" or "we") for the action, as long as the context makes it obvious. The sentence clearly implies "Because [someone] pulled so much, the rope gave way."

Does ceduto (from cedere) mean "broken" in this context?

Exactly. You might already know cedere as "to yield," "to give in," or "to surrender." When applied to physical objects under pressure or strain (like a rope, a bridge, or a wall), it means "to give way," "to collapse," or "to snap."

Since the rope is undergoing a physical change of state, why is the auxiliary verb avere (ha ceduto) rather than essere?