Yes. If you have WP/Visa you can stay even though you are no more with employer. If employer is asking you to go back and because of that reason you quite, you are eligible for EI (Employment Insurance) as well..
Coming to BOWP, you will be eligible on April so you have to stay (not necessarily work) till April (Cant go out of Canada) and should have PR AOR # when you apply .
If you have Offer letter from other employer, you may apply for BOWP before April by attaching that offer letter and explaining your case on letter. There are good chances that officer may grant Open WP even though it is 4+ months. It may gets rejected. All up to Immigration officer.