It's possible to set both negative and positive class weights in a binary classification scenario. However, when a multi-class classification model is trained using a OVR solver, it's possible to set weight only for the positive (i.e. One) class, but the weight for the negative (i.e. Rest) class is always set to 1.
The difference can be seen in https://github.com/cjlin1/liblinear/blob/master/linear.cpp#L2552 where train_one uses both weights and https://github.com/cjlin1/liblinear/blob/master/linear.cpp#L2578 where param->C is used. That corresponds to always using 1 as a weight.
That doesn't allow class weight normalization, and unnormalized weights bias the C term.