Car keeps cutting off when idling.

My car keeps cutting off when idle at stop lights and also when driving at low speeds. I just did an inspection of the battery and surrounding areas and I found a little red wire that's attached to the distribution box. It is dangling free on the other end. It is brittle for when I grabbed it, I could feel it breaking easily as if it is rotted. I can't tell where the other end was attached. Does the other end go to the battery? Can it be the cause of my problem? Please help! I just retired and I'm living on social security. It would be a strain financially to even have it put on the machine at a dealership to see what the problem is, let alone pay for an expensive repair. I would appreciate any help I can get on this matter.
God bless and thanks. I would be happy to send a donation on the 3rd of the next month. I'm on a monthly fixed income(social security)