When a site reaches its resource limit on a server with resource management tools like LVE (Lightweight Virtual Environment), several outcomes may occur, depending on how the system is configured:

1. Performance Degradation: The most common consequence is that the site's performance will start to degrade. This can manifest as slower loading times, unresponsive pages, or timeouts.

2. CPU Throttling: If the site exceeds its allocated CPU resources, it may experience CPU throttling. This means that the server will limit the amount of CPU time the site's processes can use, potentially slowing down the execution of scripts and applications.

3. Memory Constraints: If the site consumes more memory than it's allowed, it may experience issues like slower database queries, failed database connections, or even crashes if it tries to allocate more memory than it's allowed.

4. I/O Limitations: Excessive I/O (Input/Output) operations can lead to delays in reading or writing data to disk. This can result in slower page loads, especially for sites that rely heavily on database interactions.

5. Inode Limitations: Some servers have limits on the number of files (inodes) a site can have. If this limit is reached, it can prevent the creation of new files, which can lead to errors or site malfunctions.

6. Temporary Suspension: In some cases, if a site consistently exceeds its resource limits, it may be temporarily suspended to prevent it from impacting other users on the server.

7. Error Messages: Users visiting the site may see error messages, such as 500 Internal Server Error or 503 Service Unavailable, indicating that the server is having trouble fulfilling the request.

8. Logging and Alerts: The server's logging system may record events related to resource overages. Additionally, administrators may receive alerts or notifications about resource usage.

9. Isolation or Termination: Depending on the server's configuration, the system may isolate the site, limiting its impact on other users, or even terminate its processes to prevent further resource consumption.

10. Manual Intervention: In some cases, the server administrator may need to intervene to address the resource usage issue. This could involve investigating the cause of the overages and taking appropriate action, such as optimizing the site or upgrading the hosting plan.