If you have your SIN, and you obtain a Canadian drivers license and health card while you still have a valid PR card, there should be no significant problems staying in Canada after the PR card expires . . . that is, no problem living in Canada without a currently valid PR card. There is NO requirement to have a valid PR card EXCEPT to show when traveling back to Canada from abroad.
Some government services and licensing require proof of status in Canada. Provincial drivers licensing and health care coverage for example. Once you have obtained these using a valid PR card, there should be NO problems with these going forward.
BUT PRIVATE EMPLOYERS CHOOSE JOB REQUIREMENTS
What private employers require is largely up to them. Technically your SIN should be sufficient proof of status to work in Canada. But there are occasional anecdotal reports in the forum about certain employers requiring employees to have a valid PR card. Perhaps the CoPR will suffice, showing you are in fact a landed PERMANENT Resident. Might be a bit tricky, to do so politely, but perhaps a reminder that "permanent" means, well, PERMANENT (unless and until it is taken away). BUT overall, there are NOT many reports of employers being unreasonable about this . . . except . . .
. . . except there is more risk of this when obtaining a NEW job. That is, more employers might ask for proof of status to live and work in Canada during the hiring process. The forum does NOT have enough reports, quantitatively, to know whether this is a significant or common issue. Again, however, technically your SIN and CoPR should suffice. Perhaps showing an expired PR card and explaining that an application to renew is pending, but further explaining that you really do not need a new PR card, and you are mostly waiting to when you are eligible and can apply for citizenship. Or something to such effect.
BUT private employers can generally impose whatever conditions on employment they choose EXCEPT for criteria that violates Canadian anti-discrimination or other labour laws, which I am not much familiar with, provincially or federally.