I know lots of people whose work visa renewals came late. Once you file for the renewal, you are legally allowed to stay in the US while it is processed. Everyone I know in this situation continued to work and their pay was withheld until the new card came. Their pay was then released.
This is illegal (if you're on OPT/F1/J1), and will get you deported. You can't work when you don't have a work permit - and you can't get paid later for a time when you didn't have a work permit. (H1B, L1 and other work visas have a different process and a different set of rules).
