in Venezuela they stamp a full page into your passport with the bike details, I asked the custom officer not to do it because I was running out of pages, but he wanted some money for not putting the stamp, so I let him stamp and waste a page.
Leaving Venezuela (I left overland and also by air, of course not at the same time) nobody was intrested to see the stamp. I never got an exit stamp for the bike, not even in Caracas in the airport customs. Should be no problem leaving the country without the bike.
In Colombia they dont stamp your passport at all for the bike. You get a white paper with the bike details, thats it. So you can leave the bike behind, no problem. Only when you return and than leave the country with the bike, it could be a problem, because the white paper is only valid for I think three months.
So, you see, in both countries it is possible for you to leave your bike behind.
But not legal.