Sometimes the datasheet for TI High Side Switch will have a section called “extended voltage range” like below:
The “extended supply voltage” is only for transient conditions such as cold crank (less than minimum nominal supply voltage) and surge/load dump (greater than the maximum nominal supply voltage). The device should only be operated in DC steady state loading conditions in the “nominal supply voltage” range. Protection features such as current limit and short-circuit reliability cannot be guaranteed outside of the nominal range and operating in steady state condition outside the “nominal” range is not supported. In some cases, the Rds(on) value will increase in extended operating range like below.
In conclusion, the extended voltage range is intended to deal with transient conditions. The device should be operated with DC bus voltage within the nominal supply voltage range for a reliable operation.