Alzner had serious groin damage before his time here was up. He never fully recovered from that, much like Laich before him, though I think Laich's situation was even more severe. I'm sure that was why the club never tried to do anything with him, but just let him go. Why MTL gave him that big contract is beyond me, but in a sense "it's a reward" for the hard work he did in his years here. It just wasn't us that gave him the reward.
A dirty little secret is that, if the Caps had tried to trade Alzner they would have had to disclose all their medical records on him upon request, because they would be trying to exchange asset for asset. But once someone becomes an unrestricted FA they are no longer under your control, so you don't have to show anybody anything. It is up to them to do due diligence.
The Caps CAN'T acquire Alzner and stay under the salary cap. Now they might be able to keep him temporarily if Kuzy/Oshie were put on LTIR, but then they'd have a problem on the day they came off.