It's not a zero chance. All that would need to happen is:
1) Karlsson says he wants to extend but negotiations take longer than expected
2) Season begins. Sens do really well, but still can't come to terms with Karlsson as the season goes on.
3) Trade deadline comes and goes. EK not traded because Sens are in a great playoff spot.
Not saying it will happen, but that's a totally possible scenario.
Honestly that's not plausible in the slightest for this team, and for most teams. The Islanders letting JT get where he is is an example of what teams try to avoid unless they expect to be a playoff team ahead of the season, and if the relationship is good enough to assume an extension. We have neither of those things going for us.
We're not going into the season with EK not signed, I don't believe that for a second. Like Turris, if a deal can't get done we'll trade him, and it will be earlier rather than later to maximize all of the rosters with space.
People bring up Chara, but that was a circumstance where we were one of the best teams in the league, and a chance at a good playoff run was worth not trading either defence man. It also backfired on us and I doubt we'll do it again.
Also, we have seen what waiting to trade has done to a player's values over the years, as it takes us from a position of power to a position of weakness, meanwhile, in the offseason we're in a position of power versus weakness. There is no reason for this team to lose top value for EK on the off chance that we may be able to convince him to sign after not getting g it done all summer.
While technically possible, I wouldn't want, or expect PD to allow this horrible circumstance to occur.
