If the antibiotic-resistance genes are present on plasmids, then the bacterial population must be exposed to antibiotics constantly for the genes to remain expressed. Otherwise, the plasmids get discarded after several generations. I'm not sure about genomic genes
Wild-type modules of resistance genes are often induced by the antibiotic itself so that they are not expressed in the absence of antibiotics (ex. the tet resistance efflux pump which is repressed by the tet repressor). However, this is not always the case and some resistance genes are expressed also in the absence of the antibiotic. In addition, many resistance genes used on plasmids or constructs are not under their native promoter and are often constitutively expressed. Bottom line: it really depends on the particular regulation of the resistance gene that you are studying.
I agree with Nathalie Q Balaban that it depends upon the resistance gene/cluster you are considering. However I think that even those whose expression is induced by the antibiotic do not have zero expression in its absence but rather just low. This is for single copy of the resistance gene, once you get it on high copy plasmids then I think in most cases your basal level is higher (but there may be some exceptions to that).
I gree with Nathalie Q Balaban. resistance genes are often induced by the antibiotic itself so that they are not expressed in the absence of antibiotics.