I get the feeling D2's going to be a massive reset button and you wont need to have played D1 to understand what's going on. It'll probably serve a function like The Hobbit to D2's Lord of the Rings: useful for backstory info, but ultimately not needed. Destiny 1 will likely keep running for a year or two at least. It'd be unwise to kill it immediately, as you'll have players who will not move to D2 on day one and will keep playing D1, especially whoever might still be playing on 360/PS3. Further, by keeping it running they may be able to sell more copies of D1 for those who want "to get the full story" (such that it is). I know guys who got into Halo with Reach and started buying copies of the older games for the same reason. It happens. I doubt it'll be updated though; at best they'll cycle in Iron Banner once in a while.

They said destiny 1 will continue for the foreseeable future. It will stick around in its last updated form probably for a year or so.

You can still play it but they most likely wont continue to update it.