It is not recommended to use proc_open() to directly handle WebSocket connections within a standard, short-lived PHP web request. The primary function of proc_open() is for inter-process communication with other programs via standard input/output pipes, not for managing persistent network protocols like WebSockets.
WebSockets require a long-running, persistent process and an event loop to manage continuous, full-duplex communication, which is fundamentally different from how traditional PHP scripts execute.
Recommended Approach: Separate WebSocket Server
The standard and most robust solution is to run a dedicated WebSocket server separately from your main PHP application, using a specialized library or a different technology:

   Use a PHP WebSocket Library: Libraries like Ratchet or OpenSwoole provide the necessary event-driven architecture to handle WebSocket connections efficiently in a long-running PHP process. You would run this server from the command line, separate from your web server (Apache/Nginx).
   Use another Technology: Many developers prefer to use Node.js or Python for the WebSocket server, as these languages have built-in support for event loops and concurrency.
   Use a Reverse Proxy: A reverse proxy (like Nginx or HAProxy) can be used to route WebSocket traffic (ws:// or wss://) to the dedicated WebSocket server and normal HTTP traffic to your standard PHP web server.

How proc_open() Relates
You can use proc_open() in the main PHP application to spawn this separate WebSocket server process or to communicate with an already running one via a message queue (e.g., Redis, RabbitMQ).

   Spawning the process: Your main script could use proc_open() to start the dedicated WebSocket server script as a background process.
   Inter-process communication: Once running, the main PHP script cannot directly "speak" the WebSocket protocol to the external process's pipes. Instead, the external WebSocket server would need to communicate with the main application's backend using an internal mechanism like a database, a message queue, or a dedicated internal TCP socket.

Summary
Method
  Description  Feasibility for WebSockets
proc_open() directly  Trying to implement the WebSocket protocol over proc_open() pipes.  Not feasible/practical
Dedicated Library (e.g., Ratchet)  Running a separate, long-lived PHP script with a specialized library.  Recommended
External Service/Proxy  Using an external service (Pusher, Ably) or a reverse proxy to manage connections.  Recommended for robust/scalable solutions