One time I was on a business trip in St. Petersburg Russia, when my company called and told me they needed me to do a presentation in Rio, Brazil.

I was booked LED - CDG - GIG on Air France.

Nobody ever mentioned to me that Canadians need a visa for Brazil, and I didn't ask. Oops. Only make that mistake once!

Air France never checked for a visa at CDG and let me board. When I landed in GIG and they discovered I was visa-less I was kept in a holding area and I was told Air France would be flying me back on the next flight because I was their responsibility. I didn't want to fly back to CDG, and the flight I was supposed to take two days hence back to Canada via the US (US Airways as I recall?) had already left on that day. The Brazilian border police guy was sympathetic to the confused and jetlagged Canadian and agreed to escort me around security and customs land side so I could use my credit card, buy another ticket on a flight that night and then escorted me back around security and customs airside where he left me to wait until my flight left. He did come back and check to make sure I got on the plane.

TLDR: You are the airlines responsibility, and they have to fly you back from where you came unless you manage to get someone sympathetic and make other arrangements.

I do have a Brazilian visa now