Here is an interesting example for how changed stalemate values could apply.
It's an engine game played in the IC engine hall. White has clear advantage, as acknowledged by Black's Stockfish (1.52/46), and it is White's turn to move. White's evals are much higher (3.32/51), as he is running a modified Stockfish with changed stalemate values. There seems to be no way for White to win this game, so the engine favours to stalemate Black by transforming the position into an endgame K+P vs K.
Unfortunately, after reaching the advantageous endgame the "auto draw" functions rules on a draw and prevents White from stalemating Black.
The example shows two things:
1) A typical position, where advantage is not big enough to mate, but to force a stalemate (by zugzwang).
2) The auto draw function should not apply for centaur tours, as far as it is based on "insufficient material" (with the only exception K vs K).
It also shows, that a modified engine is able to evaluate the chances of stalemate, but it is still an open question, whether in other cases it might handicap itself as going for a stalemate, when it would still have chances to achieve a mate. Also it's not clear, how playing without tablebases affects the chances.
