The only way he'll stay IMO is if the club can't secure another target, and if Silva is still in the mix, they'll appoint him over another year of Sam I think (in the event Fonseca, others, say no).
What's critical is timing. We need clear answers / commitment from those interested and we need them fast. We may already have gotten a commitment from somebody pending them finishing in their current role to the end of the season, though if such is the case, it would lead me to think that's Fonseca and not Silva, as there is nothing stopping us with him, if both sides want the move.
The only scenario I can countenance in which its better for Allardyce to stay another year rather than leave is if he is still here by the end of May / very early June (even that's very late). We then go into the WC and absolutely cannot repeat the farce of last October/November and be pinning the tail on the donkey in trying to get a new manager.
The board, all of them, will again be shown up for all to see if they make another mess of this.