I haven't seen this personally... and since the "chrome didn't shutdown cleanly" is a flag
stored per each profile, the migration should never affect the value.
https://cs.chromium.org/chromium/src/chrome/browser/ui/startup/startup_browser_creator.cc?type=cs&l=933
https://cs.chromium.org/chromium/src/chrome/browser/profiles/profile_impl.cc?type=cs&l=904

I guess simply the previous session before the migration was crashing?

For instance, the linked feedback report is uploading one crash report presumably from the previous session

2017-06-13T10:02:02.718012+01:00 INFO cryptohomed[2851]: Migrating to dircrypto.
...
2017-06-13T10:16:00.465777+01:00 NOTICE crash_sender[6048]: Crash report receipt ID ef1caa6e40000000
2017-06-13T10:16:00.473256+01:00 NOTICE crash_sender[6050]: Successfully sent crash /home/chronos/crash/chrome.20170612.185142.25499.meta and removing.
2017-06-13T10:16:00.491941+01:00 INFO periodic_scheduler[6054]: crash_sender: job completed
...
2017-06-13T10:17:30.673507+01:00 INFO cryptohomed[2851]: Migration done.

The crash http://crash/ef1caa6e40000000 is at shutdown time, so the previous session did not shut down cleanly indeed.

I tried to reproduce this locally but couldn't. I think we're doing fine.