Ok so, when they are young, they eat. But when they are full grown, they don't. Mayflies don't eat when they are full grown - and they don't have mouths. And they're incredibly primordial compared to an enormously complex organism like the Alien; so why wouldn't Aliens have their teeth fall off when they age?
To kill the threats, they kind'a have four sets of claws, tail and, primarily, inner jaw.