Couple thoughts.
Pesce: the only way I see him staying is if he takes a really big $ discount or takes a moderate discount but agrees to at most a 3 year contract, neither of which is in his best interest. In my mind it comes down to the Borg factoring in the risk that his play falls off a cliff due to injury or just general physical breakdown.
Guentzal: I see a better chance of the Borg signing him than Pesce. Would likely only happen if Guentzal evaluates UFA offers and takes a decent discount to re-sign with Carolina. I believe he's sincere in wanting to stay here, the question will be his calculus of the value of team/ city "fit" vs. $. But he's made almost $33m in his career, and depending on his othr UFA offers I could see him considering taking a "Stamkos" with the Canes to make sure to maximize his enjoyment of most of the rest of his career, even though he only spent a couple months with the Canes.
Necas: gone if another team offers up a "hockey trade" that would help the Canes win now, otherwise they'll leverage his RFA status to keep him here for now.
Chatfield: decent chance they keep him.
Jarvis: no need for discussion.
Skjei: only if he signs at a pretty good discount. Not nearly as much of a need on the left side, but also nowhere near the risk of falloff as Pesce.
Turbo: would need to take a really big discount, big enough that he probably shouldn't consider it.
TDA: he gone.