When an animal is in your care and is injured or dies are you liable and covered?

When I look after someone's pet if they are on vacation, I have them write out a note giving me the legal right to take their dog to a vet if needed, and also, I have the right to make choices in the case of emergency. I have them date and sign it. Accidents happen, so, no, usually you aren't responsible in most cases if the dog gets sick. If the dog/cat was run over by a car most people won't sue you, but you should offer to pay for the next pet they get just for your own conscience sake.