Eligibility to stay


My h1 is about to expire on 13th Dec, 2019. My current employer had declined to file for an extension as my current project is ending soon. I have found another project recently, they have filed for my lca last week and we are hoping to get the approval this week.
My question is if we submit the application within 2 days, can i stay in the US without it being termed illegal? If so until what date will i be eligible to stay legally until i get my receipt notice? Also, i am not sure yet if they will be doing a premium processing, if they don’t can i work just on receipt notice in the new project?

Thanks in advance!