「金の切れ目が縁の切れ目」（かねの きれめが えんの きれめ） tells us that many relationships are based on money.

Many people are around you as long as you have money; many leave you as soon as you lose money.

In this saying, 「目」（め） is used as a suffix to mean the situation where things may change. So, 「切れ目」（きれめ） is the situation where something breaks in two.