Working in USA and staying in Canada

I have a valid H1B visa and a valid Canada PR, My Canada PR is near to expiry and my green card process is not started in USA, it may get completed by next year until then I can work on H1B. My worry is if my employer doesn’t start the green card process and my PR validity is also over, I have to travel back to my country which I don’t want to. Can I stay in Canada border city (Canada PR) and travel to work to USA (on H1B).