From antiquity up until the industrial era, rope was made by hand but using time-saving tools, from commonly/widely farmed fiber crops such as hemp and flax. The process of retting the fibers from the harvested crop, twisting them into strands and twisting the strands together into rope is time consuming but not complicated or difficult to learn.

These crops were grown for both clothing and food (both flax and hemp have edible seeds), and we know that rope was a common item at least in rural areas, as there are depictions of medieval oxen hauling a plow with a rope dating from the 1300's.

Hopefully someone can chime in with a direct source for a price, but while it's likely pre-industrial rope cost more than the machine-produced nylon rope we buy at hardware chains today, it was a common item made from an abundant, readily available resource that did not require great specialist knowledge or skill to produce.

Further, although today we might shrug our shoulders and just buy another rope, we should remember that in the past splicing two lengths of rope together was common practice, and a mere cut could thereby be repaired.

With that in mind, we can say that by the time of the the Musketeers, set in the 1620's, a mere severed rope would incur a relatively low repair cost. Indeed by that time, the owner of the logs might be more concerned with damage to the wood from the drop, depending on the species of tree and the intended purpose.

As for ships, we know that at least naval ships in the age of sail carried spare rope because some inventories and logbooks have survived. Old rope and pitch were used to seal (and re-seal) the gaps between planks in sailing ships. Given that, and that not having an important piece of rigging functional could easily become a life-and-death issue for everyone on board, it's difficult to imagine a ship of any significant size in the age of sail having no spare rope on board.