When subs get bound, you lose their attack and the ability to activate their skill. When leaders get bound, it's the same except you also lose access to their leader skill. If the leader skill includes hp multiplication, your max hp goes down temporarily, which can reduce your current hp as well if it was higher than the lowered max hp. Note that active skill cooldowns continue to charge when a monster is bound.
This doesn't automatically kill you, and since bind takes up their attack it COULD save your life. It's pretty bad, though, and I wouldn't recommend bringing a mono team into a bind situation unless you're confident about burning them down first. If your whole team gets bound, you have to match orbs until the binds wear off.
Heart orbs will still heal you regardless of bind - I have heard that RCV increases from leader skills will still be in effect when the leader is bound, but I don't know whether this is true or not.
