Yuccas get really overgrown and top heavy around here so a heavy rain or snow will cause them to fall. People remedy this problem by putting concrete in the weak parts of the trunk so maybe you can do the same for your Foxtail palm. Palms get holes in their trunks occasionally, usually it has to do with a sprinkler being close by. Larger holes can cause problems during bad storms (like hurricanes) because the weak spot can give way, but I havent seen a palm damaged by these holes other wise.
I think a little concrete should work to cover the hole, but definitely hear some other opinions first!
-Alex

Do you have any photos? Do you have any idea how the hole developed, slowly or quite rapidly? Never been a problem with mine, although I'm in a different climate to yours. But can't imagine it being anything other than some insect or other animal chewing in to it.