Am I obligated to guarantee a cow that fell into a pit I left open on my land and died, and am I negligent for leaving the pit open?

There is no liability on the owner of a well if he dug it on his own land and did not intend any harm by it, because the Prophet, peace and blessings be upon him, said: "The well is jubar (unaccountable)," meaning that the blood of whoever falls into it is in vain, and there is nothing upon its digger. This applies if he dug it on his own property or in a place owned by no one, and no harm resulted to others from his digging.