Here is the full document: https://www.govinfo.gov/content/pkg/FR-2016-11-18/pdf/2016-2... (search for "60-day nonimmigrant").
Note that during these 60-days you can then file for a change of status, and then you will still remain in-status while that request is pending (the change you file must be "non-frivolous" though!).
If you follow this route and try to change status, USCIS has the right to revoke the grace period retroactively (in cases of abuse, for example). Documentation that you were actively seeking new employment should help avoid this.
Anyway, concerned people should certainly speak to an immigration attorney (again, I am not a lawyer), but it is comforting to know that most likely we have 60 days to get our affairs in order...