No - it's not a "crime" in the sense that it is not covered by the criminal code in Canada. It falls under "Family law" which is considered [civil](https://www.courts.ca.gov/1000.htm) in Canada.

Which is not to say it can't have legal consequences the [Family Orders and Agreements Enforcement Assistance Act](https://laws-lois.justice.gc.ca/eng/acts/F-1.4/FullText.html) sets out actions and sanctions that the Canadian government can take against those who violate a court order instructing them to make support payments. This can include such things as garnishing wages/state payments and even suspending driver's licenses.

If they "run away" as you put it and aren't making payments on things like a mortgage which is in their name (wholly or partly) then this would be covered under normal civil debt proceedings the same as if they stayed and didn't pay.