Qualifying offers are tendered to players who are no longer on their entry-level deals but do not qualify as un-restricted free agents, making them restricted free agents. Teams must extend qualifying offers to restricted free agents to retain their negotiating rights and have the right of first refusal.
Notably absent* from the above list is Sean Bergenheim, one of the last remaining Milbury-era picks. Unless there's some misunderstanding -- highly unlikely, given Dale Tallon's employment in Florida -- or kiss-and-make-up in July, that means the Islanders are letting Bergy walk for nothing. Considering his qualifying offer wouldn't be much (in the ballpark of $1 million) and Bergenheim is at minimum a useful energy winger, that is not the kind of asset management I like to see.
But then again, dating back to the contentious failure to sign by training camp that led to the Wang-enforced year in exile, it's always been a rocky union between the Isles and Bergenheim. If he wants to stay in the NHL, I expect him to find a home.
As discussed in his report card here, this "Finn of mystery" was still effective 5-on-5 and one of the Islanders' few physical presences. His scoring counting numbers never matched up to his first-round billing (22nd overall, 2002), but as we detailed in that report, he never had consistent linemates this past season. And while he was once known for taking poor penalties at poor times, last season he was among the team leaders in drawing more penalties than he took (+10).
There's a lot to like about Bergenheim's game, but after eight seasons of pro hockey on either side of the Atlantic, it's also fair to wonder if he'd ever fully put it together beyond a checking line/PK role that, as others have already commented below, should be replaceable. Perhaps in the case of Bergenheim, the Islanders long-term handling of him was about as cohesive as his on-ice decision-making: Mixed, with missed opportunities all around.
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The qualified: Those whose rights are retained aren't surprising. Garth Snow recently spoke well of Lawson's ability to fill in at the NHL level "in a pinch," while Reese impressed in his brief quarter with the big club at the end of the seasons. Kohn likewise is just showing what he can do -- still up in the air, but you don't give up now -- and Moulson and Rob Schremp Hockey were of course no-brainers.