As well as avoiding the negative, characters with MCI often happen to stumble upon just what they might need for a given situation, out of the blue.
This phenomenon could be chalked up to just plain dumb luck, or perhaps more likely unrealistic writing on the creator's part. Mary Sues and their variants are often gifted with Main Character Insurance.
Generally, when this occurs, it leads to a very unrealistic and fantastical atmosphere, removing any seriousness there might have been.
Viewer A: What the hell? This character has managed to dodge bullets, stay underwater without drowning, and remain perfectly healthy in an outbreak of plague. On top of it, howcome the key to the safe was suddenly right there when everyone else has been looking for it for decades? That's just not fair.
Viewer B: Yeah, he evidently must have some sort of main character insurance. Considering the shooters killed everyone else, his friend drowned quickly, and his girlfriend is now dying of plague. If he really found that key so easily, it makes the other characters look like total idiots. Something isn't right here.