Antimicrobial resistance frequently carries a fitness cost to a pathogen, measured as a reduction in growth rate compared to the sensitive wild type, in the absence of antibiotics. Existing empirical evidence points to the following relationship between cost of resistance and virulence. If a resistant pathogen suffers a fitness cost in terms of reduced growth rate it commonly has lower virulence compared to the sensitive wild type. If this cost is absent so is the reduction in virulence. Here we show, using experimental evolution of drug resistance in the fungal human pathogen <i>Candida glabrata,</i> that reduced growth rate of resistant strains need not result in reduced virulence. Phenotypically heterogeneous populations were evolved in parallel containing highly resistant sub-population small colony variants (SCVs) alongside sensitive sub-populations. Despite their low growth rate in the absence of an antifungal drug, the SCVs did not suffer a marked alteration in virulence compared with the wild-type ancestral strain, or their co-isolated sensitive strains. This contrasts with classical theory that assumes growth rate to positively correlate with virulence. Our work thus highlights the complexity of the relationship between resistance, basic life-history traits and virulence.