The fuling village is built over a (or a set of) spawn points. Even destroying the village doesn't remove the spawn point(s). The only way to completely keep them from respawning would be to destroy the village and then cover the area with enough work benches to suppress the spawn points.

Same thing with the tar pits. To keep growths from coming back you have to drain the tar and cover the drained pit with workbenches.

Even if you do that random fulings, deathsquitoes, and lox can still spawn (especially at night) and if they do and destroy your workbenches then the spawn point is no longer suppressed.