The lease should spell out the tenant's pro-rata share of operating expenses, taxes, and insurance and should also spell out how the tenant's pro-rata share is calculated. If it is in the lease it can never change go up. So if there is a vacancy, the LL is responsible for the expenses generally assigned to the vacant unit.
Where it can get fuzzy is the fixed versus variable operating expenses. Fixed operating expenses will remain the same regardless of occupancy levels (insurance, taxes) and variable operating expenses will fluctuate with occupancy levels (utilities, repairs and maintenance). If the spaces are not separately metered or with dedicated HVAC then tenants may run the risk of paying for utilities in the vacant space and have to rely management to be responsible for turning off lights and setting HVAC to minimum levels (55 degrees in winter, off or 78 degrees in the summer). Depending on the operations of other tenants other things could fluctuate like trash, repairs and maintenance, etc.
Bottom line - tenants should be protected in the lease from their share of operating expenses, taxes, and insurance increasing due to a vacancy. Look under Additional Rent, Operating Expenses, Real Estate Taxes and Insurance clauses.