This is for an extended stay in a hostile place. By Hostile, I mean, difficult to survive. Too hot, or cold, hostile weather, like hurricanes, etc.
The first thing to consider is to stay or leave. Make the decision quickly, as the opportunity to leave may change at a moments notice. If there is a chance you must travel, set up a emergency travel bag with basic essentials like medicines, extra glasses, candy bars, etc. and water.
One question one might ask oneself is a question of weapons. Ever hunter knows it's tough to shoot live game. Most shots are less than one hundred yards away. If you have a rifle and are good with it, remember, you may only have the one shot, so shoot like your life depends on it; it just may! Using a firearm for protection is best left to professionals. If you are not trained to kill, in self defence or in combat, don't consider a firearm a good weapon.
When in the wilderness, always carry a knife. Sometimes you may need something large and sharp for any number of tasks. A small pocket knife is always handy, too.
Some like to walk with a staff, or a tall walking stick. This can be handy to test the ground ahead, or help another through a rough area. It can even be used to save a life; you could help someone out of the ice!
Think about what is used to populate your emergency "get out of town" kit. You may be surprised at what may be useful. Consider where you may go and what you may encounter on the way. Are you alone or are you also protecting loved ones.