Use some pliers and see if the corrosion can be crushed to expose the end of the elements internal ni-chrome wire... just clip around the edges... then sand the internal wire until it is clean.... strip back the wire you are holding and see if it looks clean, no corrosion... then apply solder to the element wire and black wire to "pre tin" the two connections.... then solder them together... for electrical insulation, wrap the newly soldered connection with fiberglass electrical tape.. it is heat tolerant and the new connection will last forever....
The reason the connection gave up is.... a poor connection from the factory... seems to happen on many MES smokers... poor connections cause heat and then corrosion..... once a connection is soldered properly, that condition is eliminated......
If the element ever burns out, it can easily be "un-soldered" but you won't live long enough for that to happen......
Dave
Don't worry about the end of the element getting hot... the ends may get warm but the heat doesn't get created until the electricity has traveled down the element for a small distance... it the nature of the beast.....