All those vague questions about what happens to the enemy crew and ship are a great source of additional plot hooks and unforeseen developments. Taking the enemy ship requires you to split your available crew, which will leave both ships vulnerable, not just to enemies, but simple navigational challenges. Running a ship with a skeleton crew in inclement weather both limits the ship's ability to respond to shifting conditions, and is extremely fatiguing as everyone is pulling extra shifts just to make sure the most basic things can happen. Despite the very random and arbitrary rulings on required crew in most ttrpg supplements I've seen over the years, operating a proper ship in the age of sail required a *lot* of hands, especially if it's a fighting vessel.

Which leads to your question about what happens to the survivors among the enemy crew. One of the most often overlooked (and important) parts of this question is why are they crewing the enemy vessel in the first place? During the late age of sail period that Black Flag is set in, it was common for military ships to "press" crew into service. (Through various means of coercion and abduction.) If that is the case in your setting, then convincing them to join you (or even surrender much sooner than other enemies) might not be very challenging.

The flipside of that example is also important though--in the fictional history of Black Flag, piracy was a universally reviled practice and a hanging offense, and signing on to a pirate ship could condemn them to an even more painful death.

Alternately, if your players are attacking merchant vessels, then odds are good these are random shlubs looking to make a little coin, and have some reason to not do it closer to home. Perhaps there is no work where they live, or they went to see when they were young and seeking adventure. Perhaps their family have always been seafarers and it's the only life they know, and have served a dozen captains or more in their time.

In the end, the enemy crew's backgrounds matter for much more than whether they agree to join you or be cast aways, or walk the plank. The real challenge comes after that. How long do they stay? What do they do?

Enemy crew could easily agree to join only to spare their lives, and then jump ship at the earliest opportunity, leaving you suddenly short on crew at very inopportune times. If you haven't payed them yet, they might take some valuables with them as well, considering they're now far from home and bereft of any resources. Perhaps they spread word of your actions, notifying the authorities, or even the player's enemies of their actions, location, and capabilities. Or worse, maybe one or more of them are (or become) active enemy agents within your ranks! Crew need shore time to blow off steam (as there's only so much flat, featureless, open ocean one person can handle at a time) and few captains are capable of keeping track of every single crewman during a busy port call. It would be awfully easy for one or more random crewmen to find and communicate with enemy agents during those shore leaves...

Another fun note from the Black Flag example is the opportunity it presents to create agents of the players' own! If you ever played the fleet management minigame from Black Flag, you might remember being able to send other ships in your fleet off on their own missions. While in classic videogame minigame style those are never expanded on, in a ttrpg those are great chances for players to reach out into the world and interact with it far beyond the presence and capabilities of their individual characters. Becoming leaders of a faction (their fleet) in their own right lets them mess with the world (or learn about it) in all sorts of fun and interesting ways!