Well firstly, to put this question in perspective, Ships in the Napoleonic wars rarely sank in action. A prototypical engagement would involve an exchange of fire at long range or, more likely, very close range followed by either a surrender or boarding action. Gunnery targets were the ships masts and rigging and its gundecks, causing the ship to lose the ability to maneuver or return fire. Once these were gone it would be disabled and unable to resist or escape. Hitting a ship "between wind and water" in such a way to compromise it's buoyancy or seaworthiness was generally not an optimum strategy because a wooden ship could take quite a while to sink. Most ships lost to the enemy were captured, rather than outright sunk, or at the very least captured first and then abandoned by the victor as unsalvageable. In this case, the crew would be treated as prisoners and could be exchanged for prisoners captured by the other side. Captured ships and prisoners were valuable for both for prestige, military, and economic value. Prize money was paid for them to officers and men, so there was incentive to avoid wanton destruction.

However, it was possible for a Napoleonic warship to be destroyed suddenly, either by fire or heavy weather. If a fire broke out as a result of gunfire, and was not quickly put out, it could spread to the powder magazine. Since Naval guns of the time mostly fired solid shot, rather than explosive projectiles, this was rare. L'Orient at the battle of the Nile is one of the more famous examples. Also, sailing ships that engaged in a fight during stormy weather could cause either or both ships to wreck. [Here is one such example] (http://en.wikipedia.org/wiki/Action_of_13_January_1797) During cases of fire, explosion, or storm, it was very difficult for enemy ships to safely rescue sailors. This often meant very serious casualties.

It was generally recognized as a moral obligation of sailors to rescue other sailors, even those of the enemy. The sudden attacks of aircraft or submarines (fear of which became the pretext in WWI and WWII to abandon men) of course did not exist, so warships could generally risk taking time to rescue their opponents if they found themselves in the sea.