Yes they can have strokes, but some other things that might cause paralysis or severe lameness are Mareks disease, botulism, lead poisoning, and mold or aflatoxin poisoning. Mareks usually affects young birds in the first 6-8 months, but older birds who have recently been exposed to a new flock member or wild bird who is a carrier. Botulism comes from eating the remains of a dead fish or animal, or rotted vegetation that has been buried or without air. It sounds very grave, but I hope she suddenly starts drinking for you.