In Canada, can someone with Power of Attorney begin bankruptcy proceedings on the behalf of the estate they are representing?

Probably, but you will need an attorney to guide you through the process. So, before you go filing papers with a court, consult an attorney.

very tricky question -- in general, under English based law, the estate of a deceased person does not file for bankruptcy since Probate law controls the order of distribution.

there are other types of estates, but if that's what you're asking about, you need to be more specific.

Power of Attorney means that individual has full legal responsibility over the affairs and finances of the other person, so yes