Termite, e.g. (4)
(Other definitions for borer that I've seen before include "Drill" , "Insect tunnelling into plant" , "creature entering wood" , "Destructive worm, mollusc or insect" , "Tunnelling worm or insect" .)
(Other definitions for pest that I've seen before include "Constant nuisance" , "Annoyance" , "Annoying person" , "Destructive creature" , "Troublesome man or animal" .)