Foreverdorks, I just don't see how that would work logistically. How would you determine that he left the girl because she was pregnant? Maybe he left because they fought too much, or she smelled, or he wanted to be alone. And at what point would you stop enforcing this rule? Once the baby is born, can he leave? Once the baby is five years old, can he leave? Once the child is 18? Never? I mean, it sounds like you are outlawing divorce. (Or, if they are unmarried, prohibiting a breakup - which is much harder to define.) It would be pretty easy to get around, in that case. "Oh, we're still together, I'm just... living somewhere else indefinitely..." or "The only job I could find was a Taco Bell on the other side of the country, but I didn't 'leave' her."
Logistically, what did you envision? We already have child support laws in the U.S., and you can be jailed for failure to pay child support. Is there not a similar system in Canada?