Let me start by saying that I don't have a problem with the neighbor replacing the fence, except that I noticed when they were done last night they decided to make the section between our homes about 8 feet shorter than before. They didn't notify me and now there is an eight foot gap between their fence and the front of our fence. To me this poses a security risk. Anyone and anything can get into our yard now, and we don't have the money to put up new fencing. Do I have any recourse here?

Assuming that your neighbor's fence is on your neighbor's property (not yours), then no - you have no recourse. I assume that your neighborhood has no homeowners' association rules regarding fences being required (which would be unusual).

... they decided to make the section between our homes about 8 feet shorter than before. They didn't notify me and now there is an eight foot gap between their fence and the front of our fence. ...

I can't quite figure out exactly what you are saying. As Ebaines has said, it depends on whose fence it is: theirs or yours. And the ownership of the fence generally depends on whose property it's on.

Near as I can figure, you are saying that they replaced some fence which had separated your lots, and built the new fence 8 feet further away from the lot line. The gap would be between the end of your front (facing the street, possibly) fence and the end of the new fence.

Again, if the old fence was on your property, or along the lot-line, you can ask them to make it right. Otherwise, no. In fact, if any portion of your front fence is on their property, they would be within their rights to remove that portion too.

As long as their fence is entirely on their property you have no recourse. What you CAN do is offer to split the cost of an 8 foot section to cover that gap.