As things such as the power grid and other utilities are not monitored or repaired they will begin to break down as power outages from things such as downed power lines will spread.
People you meet will be more desperate when gathering supplies so hopefully by now you have weapons to protect yourself. There is also likely to be groups of people that have banded together to protect themselves but you as an outside have to be careful once you see these groups;
The groups could be friendly or just as easily be hostile and want to take your supplies by force. I would suggest once you have your small group that you can hopefully trust, you should be very wary of other groups.
If you and your group have managed to get a base built that you can defend apart from the supplies that you have already gathered such as food and weapons you have to think other things you might need; As the utilities break down you have to think about generators and the fuel for them as well as storage of water as services stop working.