If u cut my tail I am a Fruit

”I live in water
if you cut my tail i am a fruit
if you cut my head I am at your door
if you cut both then i am with you all the time?
What is this thing” ….

Pearl- lives in water
Pear (cut off tail or “L”) – a fruit
Earl (cut off head, or “P”) – at your door
Ear (cut of both P & L)- you have an ear that is with you