Our definition of No-Kill is simple: True animal welfare societies treat the animals as they would their own beloved pets. No animal is killed except to end unrelievable suffering. If the animal has been accepted by the society then the society must not excuse killing it on the grounds of lack of money or resources. No animal ought to be accepted if the outcome may be death because more animals have been accepted than there is space or money for. No animal should be killed for space to make room for new animals that may be more sellable or which do not require extraordinary expenses. To kill animals for those reasons is animal-disposal, not animal-welfare. Behaviour problems are not valid reasons to kill, not if the society has accepted the animal into its care.
We can define No-Kill in no better ways than so many others have. Read other definitions of No-Kill.