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 in Canada.
Which is not to say it can't have legal consequences the Family Orders and Agreements Enforcement Assistance Act 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.