My guinea pig died as he didn't recover from local anaesthetic?

hi, I noticed a couple of day ago a big lump under my guinea pigs chin,so my dad phoned his mum(she used to work with pets) and her best guess was that it was a tooth abscess. As earlier my guinea pig chipped his bottom tooth,it was hal it's original size and the middle part of the tooth was exposed. So dad got him a vet appointment the following morning,he got an operation and the abscess was burst or something,they told us on the phone that he had just woken up after the operation,later they decided to keep him overnight to recover from the local anesthetic. Dad phoned me this morning and told me he was dead ... :'(. He said that Leo(my wee piggy) hadn't recovered from the local anesthetic and died during the night. My dad buried him a few hours ago. I am wandering why is it that small animals often can't recover from local anesthetic? Why use it if there is a risk of death? Can't the vet use something else? thanks.