Yes, it is possible for someone to sue a website for publishing false content about them, but there are several important factors to consider. Generally, these claims are based on defamation, which can take the form of slander (spoken statements) or libel (written statements). Here are some key points to keep in mind:

1. Elements of Defamation:
   • False Statement: The statement must be false. Truth is typically a defense to defamation claims.
   • Publication: The statement must have been published or communicated to a third party.
   • Harm: The statement must have caused harm to the plaintiff's reputation.
   • Fault: Depending on the plaintiff's status (e.g., public figure vs. private individual), they may need to prove negligence or actual malice (knowledge that the statement was false or reckless disregard for the truth).
      
2. Defenses:
   • Truth: If the content is true, it typically cannot be considered defamatory.
   • Opinion vs. Fact: Opinions are generally protected and not actionable as defamation.
   • Absolute and Qualified Privilege: In some circumstances, certain statements are absolutely or conditionally privileged, meaning they cannot give rise to a defamation claim.
      
3. Section 230 of the Communications Decency Act (CDA):
   • Protection for Websites: In the United States, Section 230 provides immunity to online platforms from liability for user-generated content. This means that if someone else posts false information about you on a website, you often cannot sue the website itself as long as they did not create or substantially edit the content.
   • Exceptions: There are exceptions to this immunity, particularly concerning federal criminal law and intellectual property claims, but defamation claims against the website itself are generally protected under Section 230.
      
4. Who to Sue:
   • If you believe that false information about you has been published online, you may need to focus on suing the person who made the false statement rather than the platform that published it. However, if a website is involved in creating or endorsing the false content, you might have a claim against them.
      
5. Jurisdiction:
   • The applicable jurisdiction (which court has authority) is crucial, especially in cases involving websites that may be based in different locations from the person filing the suit.
      
6. Damages:
   • In a successful defamation lawsuit, a plaintiff may be entitled to compensatory damages (for economic losses and emotional distress), punitive damages, and possibly injunctive relief (an order to stop further publication of the false information).
      
7. Practical Considerations:
   • Cost and Time: Legal action can be costly and time-consuming. It's essential to consider whether the potential outcomes justify these resources.
   • Reputation Management: Sometimes, addressing the issue through other means (like a retraction request, public response, or mediation) may be more effective.

Conclusion:
While it is possible to sue for false content published about you, the likelihood of success depends on specific legal factors, including the nature of the statements, the entity being sued, and the jurisdiction involved. Consulting with a legal professional specializing in defamation law is advisable to assess the strength of your case and the best approach to take.