In a case like this, it's a mistake to simply say, "Don't worry," any personal information out in circulation could be misused in some way. However, the authorities are not worried about this sort of thing, because, for the purposes of identification, a photocopy of a passport cannot be used. It's simply a handy record in case your passport is lost or stolen, or when a hotel clerk needs to prove that he/she verified your passport/visa status.
If a passport is reported lost or stolen, the passport number is entered into security databases, so that someone using the passport will be stopped. I'd imagine the government would rather not do that in a situation like this - it might only cause problems for you (or them).
If you wanted to report the passport as lost anyway, just to be on the safe side? The form you file with the government is treated as a sworn statement, and possession of that lost/stolen item becomes a crime. As the passport actually belongs to the government, destroying it is also a crime. They don't want people reporting these things as lost/stolen unless they really are.
Might someone use a photocopy of a passport as a way of creating a false identity? Perhaps, but I haven't found anything online at identity theft sites, etc. that indicates that it's a major concern. The U.S. Federal Trade Commission has a site dedicated to identity theft
, and the Canadian government is likely to have something similar. I'd check with them, rather than the folks who issue passports, to see what possible consequences could be.