Highly unlikely in any Western, civilised country. An engine out at takeoff, even on a 4 engine aircraft is cause for aborting the takeoff, if takeoff decision speed (V1) hasn't been reached.
But if V1 has been exceeded and the aircraft is airborne and one engine has failed, that would normally mean a return to the airport (however, fuel may have to be burnt off or dumped to get down to maximum landing weight). But in 3rd world countries - anything goes.
Qantas had a spectacular loss of a Lockheed Super Constellation at Mauritius in 1960. Fully loaded for the trip to Australia, one engine failed in a highly destructive manner, just prior to V1.
Indecision by the Captain and a lack of communication between the crew and the engineer saw the takeoff abort delayed, and the Super Constellation failed to stop in time, ran off the end of the runway at high speed and crashed into a dirt bank, then fell into a low gully.
Everyone got off with minor injuries, although one person broke a leg when jumping out - however, with 10,000 gallons of high octane petrol in the tanks, it didn't take long for the Super Constellation to catch fire and burn right out.
The poor firefighting response didn't help, the Mauritius airport firefighting team wasn't equipped with fire trucks that could traverse rough terrain, so they failed in their efforts to put the fire out.
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