For a family of nonadditive nonmonotone set functions whose domain is not a \(\sigma\)-ring, we prove a criterion under which set functions of a family \(\Phi=\{\phi\}\) have the property of uniform lack of a slipping load under the condition that each function \(\phi\in\Phi\) does not have a slipping load. We also consider a problem on the extension of the property of uniform lack of a slipping load under the extension of set functions from a multiplicative class of sets P to the multiplicative class \(\Sigma\supset\text{P}\).