We assume standard (P1BN3R5Q8) value (personally I prefer 1,3,3,4.5,9 but so there).
To get a drawn position with maximum material difference, not caring about that it's illegal, we just have to plaster the field with bQs and shield the wK in the corner with a bR diagonally, plus bB or bN at the sides. This position is an immediate stalemate, no matter who has the move. (Value: 3+3+5+(64-5)*8=483)
"Improve" this position, still maximum material difference, such that the position can be played forever with help play (ignoring the dead, repetition, and 50 move rule which will cut this "play" short in this order!). This includes the possibility that Black has enough at some time and stalemates White (or self after capture) after all. Stalemate just may not be forced. Feel free to choose who has the move, but choose wisely (insert fiendish laughter). (Feel also free to give an additional position where no side can force a stalemate on self or other).
For FEN convenience, you may just omit the bQs from the diagram.