A cannonball can no doubt leave quite a gaping hole in the hull of any ship, frigate and ship of the line alike, so after a battle, how would the crewmen deal with the hull breaches that were below the waterline? With water rushing in and a friendly port some weeks away, they must have had some method to temporarily seal the breach.
To deal with large breaches below the waterline that could not be easily reached from within the ship, a technique called fothering was used. In this, a sail was filled with a mixture of oakum (tarred rope fibres, used as packing between deck planks) or rope fibres, and ashes or dung. The sail was then hauled under the ship by ropes. Using these ropes, it was manoeuvred into position over the leak, and fixed into position. As the ship sailed, the contents of the sail were washed off the sail by the flow of water, but a portion of it was carried into the leak, blocking it. Small breaches could simply be dealt with by the ship's pumps. Ships carried pumps because the joins between the planks from which they were made were not perfect. Small leaks were common, especially after bad weather, and so pumps were needed to empty the bilges of whatever had leaked in, and could typically keep up with battle damage.
In addition to the fothering method described above, battle damage was dealt with temporarily by plugs (conveniently pre-made for common cannonball sizes) wrapped in oakum and driven in with a hammer.
Most below-waterline battle damage could be later repaired by putting the ship on the opposite tack, so it would lean away from the damage and bring it above the waterline.
Roundshot of the age of sail didn't really have enough punch to actually go through the water to any real degree and still breach the hull in most cases, so the way shot holes would end up below the waterline is by hitting very low on the hull as the targeted ship was heeled away, or cresting a wave.