Orphaned Claude processes when parent terminal is killed

Description

When Claude Code is running inside an IDE terminal (e.g., Zed) and the IDE is killed/closed, the Claude process becomes orphaned instead of exiting cleanly.

Reproduction

1. Open Zed IDE (or similar)
2. Run claude in the integrated terminal
3. Kill/close Zed
4. Claude process remains running, detached from any terminal

Observed behavior

$ ps -p <pid> -o pid,tty,state,command
  PID TTY      STAT COMMAND
 4754 ??       S    claude --dangerously-skip-permissions

The ?? TTY indicates the process is detached from any terminal. Multiple orphaned instances can accumulate over time, consuming significant memory (~100-200MB each).

Expected behavior

Claude should detect when its parent terminal/shell dies (via SIGHUP or polling ppid) and exit cleanly.

Environment

• macOS (Darwin 25.2.0)
• Claude Code CLI
• Zed IDE (but likely affects any IDE with integrated terminal)