they shouldnt be left for "free run" in an unfenced area, track dogs will have a strong prey drive and theyll follow a rabbit or similar sized animal right through propertylines. unfortunatly they tend to never quite get boundry training unless theres a fence involved.
they can be a little aloof like most sight hounds and sensitive, while they tend not to listen, dont shout at them or theyll sulk!
otherwise greyhounds make wonderfull pets, theyr 60mph couch potatoes in the home and will invade your couch and bed in seconds lol.
They do get cold when the temeratures drop so a sweater or jacket for chillyer days outside are a must, and for walking use a WIDE greyhound collar (their necks are deilcate and they shouldnt realy be walked on a typical collar.)
Sit is actually painfull for greyhounds for long periods on a hard surface, the bones in thier legs and hips have such little padding over them that it gets very uncomfortable. (think sleeping on a rock or large branch when your camping with no bedroll)
and a soft or orthopedic bed should be provided for a nice comfortable surface to lay/sleep on.
they are realy sweet dogs to have around, but wont do much in terms of protection, there generally sweet with everyone.
have a rabbit problem? dont worry, not for long, the greys will chase rabbits. back in the uk we lived near a farm who adopted 6 racing greys and let them chae the rabbits everyday, the dogs loved this, after about 2 months of the chase the rabbits got bored and moved on to "dog free pastures"
again though in this case fenced property is a must, the greyhounds dont usually "get" invisible boundry lines. they will also run right through an electric fence but not want to come back in.