Hmmm... I'll assume you found these examples in a book? So here's the difference: The first phrase deals with what the subject (Mr Almost-Drowning) is doing. The second deals with what is happening to Mr Almost-Drowning. This is passive voice. Still, have a good think about the above answers, as the actual grammar for the phrases sounds shaky. If the phrases are your own, try to simplify.

Ryous, come near to doing something... means "to almost" do something. come close to...has the same meaning. The verb following “come near to” is in the gerund or “ing” form. Come near to drowning… -I come near to drowning every time I swim drunk in the ocean. -I come near drowning every time I drink vodka with my friends on the boat. (The form without “to” is also used.) Or -I almost drown every time I swim after eating a big meal. The second of your examples with the verb “being” has a passive sense. (Since the second verb is in the gerund form you cannot say…come near to ‘be’ drowned) Come near to being drowned… -I come near to being drowned by the waves when I swim in deep water. -I come near being drowned by the big kids whenever I swim in the adult pool. Or -I am almost drowned in the water whenever I go to the beach, because I don’t know how to swim!

You can say: "He fell off his horse and came near TO drowning, being too heavily dressed to swim well." Nothing wrong with that per se. "Come near to be drowned" is wrong (you need a continuous after TO).

Neither usage is correct. You should say "nearly drowned" or "almost drowned".