Mentioned "Home Depot", so clearly UK.
Home Depot would have to check that the driver has a valid driving license for the car. They would have to check that the driver has third party liability insurance that covers driving this rental car, or they can offer third party liability insurance.
The first thing to check would be who caused the accident. If a drunk driver is correctly stopped at a red traffic light, and someone drives into the back of their car, the drunk driver would be guilty of driving while drunk, but would very likely not be the one causing the accident. (There was an accident two miles from my home, where one driver was drunk, had no driving license, no insurance, his car was not fit for driving, and he was innocent of an accident because none of these things caused the accident. They still threw the book at him for his offences :-) Plus a person with an alcohol or drugs problem might never drive under the influence of alcohol or drugs, or they might not have been under the influence at this particular time. Being an alcoholic or drug addict doesn't mean you can't drive. Being actually under the influence at the time you want to drive means you can't drive.
If the drunk driver caused the accident, there should be third party liability insurance, and the insurance would have to pay for the victim's damages. The exception might be if the accident was caused intentionally. The insurance would most likely try to get their money back from the driver if they caused the accident by being drunk. If there is no insurance then you might sue Home Depot because they should have made sure that there was insurance. If there was no driving license, then Home Depot might get sued by the insurance company to recover their money because Home Depot should have checked for the license.
But usually someone else would compensate the victim. You would sue Home Depot if no insurance paid, and Home Depot violated their duties of checking there is a driving license and insurance. They may have violated their duties if the renter was drunk when trying to rent the car. And if neither insurance nor Home Depot pays, you can sue the driver.