[BUG] Stale background process reminders continue after process is killed

Preflight Checklist

• [x] I have searched existing issues and this hasn't been reported yet
• [x] This is a single bug report (please file separate reports for different bugs)
• [x] I am using the latest version of Claude Code

What's Wrong?

System reminders about background bash processes (started with run_in_background: true) continue appearing even after the process has been killed, causing confusion about what's actually running

Reminders continue with "status: running" even though the process is dead

What Should Happen?

Reminders should stop after a process is terminated

Error Messages/Logs

Steps to Reproduce

a. Start a background process with the Bash tool
b. Kill the process (either through KillShell or it terminates)
c. System reminders continue appearing indefinitely about the dead process

Claude Model

Opus

Is this a regression?

Yes, this worked in a previous version

Last Working Version

_No response_

Claude Code Version

2.0.31

Platform

Anthropic API

Operating System

Other Linux

Terminal/Shell

Other

Additional Information

_No response_