if you are out of status and have no valid work permit, your employer cannot continue to employ you.
The option mentioned is for your employer to apply for LMIA (to show that no one else in Canada have your skill, experience and education to fill that position). It will cost them $1000. Once that's approved, then you can apply for a close permit.
Your status JUST expired, so you can apply to restore your status as visitor. Until your close work permit is approved, you cannot work as a visitor.
You didn't provide more details on how and what have you been doing in Canada.
If you were a student, post your question in the foreign student section.
If you were a foreign worker, post that at the worker section. This is not really about Labour Legislation. They cannot employ you because you do not work a valid work permit.