On which part? How to qualify and apply for Express Entry? If so, you can find that information in the link below. This is a points-based program and you would want to score above 500 to have some chance of being selected.
The issue is they likely won’t be able to return and getting home country emergency travel document, renewing home country passport and leaving Canada with an asylum claim in process all basically sabotage your asylum claim if you are somehow able to reenter Canada.
You really need to inform IRCC/IRB that you have left Canada. Assume you are not receiving any form of payment from Canada. If so you had to notify before you left but if not you should do so asap.