Hi guys, sorry I am confused - AEO is Arranged Employment Offer, and with this you do not start working for the Canadian employer until after your Permanent Residency under Federal Skilled Worker Category 2 is approved and visa issued.
Do you mean working with the Temporary Work Permit and a Labour Market Opinion (LMO) approved by HRDSC?
If so, the moment you are no longer working in Canada you must inform CIC, and I believe your application will be closed. I believe there is a certain grace period during which you can try to find alternative employment within Canada and a new LMO (as has been the case with CanadaJimmy), but if you actually quit the country I don't believe your application will continue to be valid.
The reason you are eligibile as a Federal Skilled Worker Category 2 is that despite not having experience in the in-demand occupation list, you have secured a job and have therefore proven your economic viability to settle in Canada (this is also the reason why proof of funds is not required for Category 2 applicants).
I believe you have to be working in Canada with a valid TMP/LMO until your residency application is complete - and if you quit your job you must inform CIC. If you fail to inform CIC then they will almost certainly find out when they come to try to validate the LMO during the visa office background checks.
Wayne.