If person was drunk and fell down steps outside of apartment complex can they sue?

It is possible for a person who fell down steps outside an apartment complex while drunk to sue for negligence, but the outcome of the lawsuit would depend on various factors, such as whether the property owner had a duty of care, if there were any hazards on the steps, and if the person's drunkenness contributed to the fall. It's best to consult with a legal professional for specific advice.