Yes, canuck, the family can of course hire and offer the job to someone else. The problem is the processing time for other Visa office is too long like that in UAE, it says 21 weeks processing but a lot of applicants there got decision within 23 or so weeks, by the time the application gets refusal, the LMIA is already expired and the caregiver (relative) can no longer re-apply and there is no other family who can hire and willing to process LMIA for him/her again.
By the way, do you have an idea how soon you will know if you get refusal? Mine is already at 19weeks, I forgot to attach a Visa office specific checklist form in my online application because there is no spot there to attach it. I actually sent everything in that checklist. The officer usually sends correspondence if there is anything missing right? I am so worried actually.
This is the form:
http://www.cic.gc.ca/english/pdf/kits/forms/IMM5894E.pdf