Wasn't West Ham playing in Europe a few seasons ago ?
Best ever run in centuries and could not keep the following season- sold all their best players.
As for Everton, I don't know they always the do it, they surely always do find a way to survive and I don't think this season would be any different, I think it's always that the tend to have some good defense, and even when they don't score the most amount of goals every season, they don't concede the most either, they always magically get their selves just about the right amount of 1-0 victories that is always in the end enough to keep them in the top flight for another season, that's why till date they remain one of the few teams to have never been relegated from the premier league.
There's always 2/3 prompted teams getting relegated back to the championship before GW 30 making it easy for Everton to survive the remaining slot. It's more about other teams taking the fall and doing them a huge favor at the end.