I guess anyone who was laid off during the ESP and will receive a salary until mid-June is not supposed to work at another employer or let Chevron know so they can stop the payments. As far as I know this does not affect the severance pay only the salary.
If the new job pays less than Chevron, which in many cases it will especially if it is outside of oil & gas, it obviously wouldn't make sense to start it until mid-June.
Are people left standing required to disclose if they have found a job ?
Can Chevron find out, and what will they do if they find out ?
Has anyone been in this situation ?