While I am not an engineer, the same could apply to my NICET status (to a much lesser extent). As such, most employers carry E&O insurance that should cover your seal as it pertains to work provided by the company. As an engineer, you may carry your own E&O insurance but as you are working for a firm, the firm's insurance should cover your work. Ask them for a copy of the insurance, talk to their agent, or ask your HR dept.
This page also covers a little bit of it:
Check with your state's PE Act and Bylaws. I'd assume once you leave, your previous employer will be forced to change the EOR on any ongoing projects.
One of those pesky ethics questions. Typically, when I have left a company I will hand off the project to another engineer even if I remain as the EOR. I will answer phone calls having to do with the project, however I am no longer being paid by the company, so anything that goes beyond answering questions about the design or design intent, the new engineer you handed off to should take care of that.
I have been lucky to always work at places where there are other qualified FPEs though. I'm not sure how you'd handle it if you did not have any peers at the former employer. You should definitely NOT be required to perform new work or even CA like shop drawing reviews or site visits if you no longer work for the company; that becomes more of a liability since you will not be under their E&O insurance.
You can always offer to consult on the project as a 1099 contractor to your former employer, or have your new employer rent you out to the old one via a T&M contract.
Good luck with this one, hard to say what to do without more specifics but I trust you will figure it out.
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