Did you ask for a supervisor and explain that as an asylee getting a passport may be difficult or impossible? Did you ever receive a physical green card? Do you have a refugee travel document or reentry permit? (those can be used like a passport)
As far as your job is concerned, I believe it is illegal for them to fire you just because the I-94 with I-551 expired. Once you present evidence of being a permanent resident for the I-9, you are authorized to work for them as long as you want regardless of the document expiring. If they won't cooperate after you explain that to them, get an immigration lawyer to give you a letter telling them that (shouldn't cost you more than about $100). Once you show them that letter and they see you have a lawyer behind you, they'll cooperate and let you keep your job.
I see the I-94 with I-551 stamp without a passport has been removed from the I-9 list. So maybe that's why they won't give you a stamped I-94. Regardless, assuming you already presented a valid document of your permanent resident status, the employer is not supposed to fire you just because that document has now expired.