Why didn't basilisk kill?

[Eddie]

No: HPFGUIDX 160415

OK, I know that everybody in Book 2: CoS who encountered the basilisk
was petrified for one reason or another (basilisk gave deadly glare
via mirror, camera, ghost, etc).  But why didn't the basilisk then go
ahead and kill/eat the victims _AFTER_ petrifying them?  Surely this
must be an ongoing problem for basilisks, that their intended dinners
keep getting petrified instead of killed?

Eddie