First, there's the Tagruato Corporation's sketchy involvement. Slusho! is a subsidiary corporation of theirs, and also the company Rob became the V.P. of and why he's having a going away party. Tagruato's a drilling company responsible for finding "Seabed's Nectar" (the stimulant in Slusho!'s drink, and also an addictive steroid of some sort responsible for the monster's extreme growth). Tagruato's CEO is in New York and then bails out just before the attack — which starts with their company's oil tanker capsizing during the first part of the attack, but leaking no oil and potentially drawing the creature in. There's also the fact that the blood of the Parasites has Seabed's Nectar in it, and there's a terrorist group called T.I.D.O. Wave responsible for attacking one of Tagruato's oil platform slightly prior to that event (connected to one of Rob's friends whose girlfriend was at the party).
The Hammer-Down protocol (i.e. bombing the everliving fuck out of Manhattan) was partially to try to kill Clover — also called the Large Scale Aggressor (LSA), but also to attempt to wipe out the extremely aggressive Human Scale Parasites (HSPs) that came off it. It was estimated there were about two thousand of them, and their bites would kill people in 20-40 mins, though no one really understands how or why yet. One of the hypothesis presented in the film for the whole events was that Clover was actually driven to land because of the HSPs attacking it — again, pointing to the fallout of actions by the shady Japanese corporations messing with those things.
All of that still doesn't touch on the fact that Clover is officially still a creature in its infancy, and the backwards audio after the credits says, "It's still alive." So, while the area around Manhattan could be free of Parasites, our main threat is still out there (and is suggested not to be one-of-a-kind). On top of that, Lily is the only main cast survivor, since she escapes on a chopper we don't see later, and don't have any detailed information about her, like we do about Rob/Jason's mom, or the guy Beth brought to the party.
What's also interesting is that, of all of the cast, when the credits roll and the characters come up, Marlena (Diamond) is the first person listed (but without her last name) — despite not appearing first in the film or even having anything close to a primary role in the group. She's totally an outsider both to the group, and unconnected to literally all other elements of the story.
I think that the fact that Lizzy Caplan and Mary-Elizabeth Winstead look very similar in these respective films could mean that that's our point of connection. This would make sense, especially since she is the only one who mentions that she was supposed to meet a group of friends who we never see in any other form in the film. It seems even more likely, since J.J. Abrams mentions that the film is "a blood relative" of the first film, rather than a sequel/prequel. This would give them a way to expand the film sideways, essentially filling out more details around it, while also adding in small elements about all the background.
At this point, my immediate guess is that Mary-Elizabeth Winstead's character is a relative of Marlena's (let's us get a last name as a connection), and she and out other guy get saved by John Goodman's character. As someone with a Fallout shelter, we get almost all of our background/conspiracy-theory-type information from him, and the imprisonment factor is the initial "monster" that we're presented with, up until her escape (attempt) — at which point we're presented with the fallout from Cloverfield. This is assumedly taking place after Sat, May 23rd when the bombs get dropped, since that happens in a period of about 6 hours, and their time in the shelter looks to be FAR longer than that. Additionally, not knowing the fate of her sister in Manhattan gives a strong motivation for escape, and means that that could just be the tip of the iceberg for her journey. (Just like the original showed next to nothing in their trailer).
Of potential note is the fact that after Marlena died from her HSP bite injury — Hud, Lily, & Rob go to Beth's apartment at 10 Columbus Circle, Manhattan and that borders Central Park. After the Hammer-Down protocol, everything gets renamed (Her apartment area as U439, and Central Park US-447), and when rewatching the film in Investigation Mode, that name stood out, especially because of the formatting, and the fact that the 10 Cloverfield Lane trailer starts with showing someone punching in just 4-8-3 (despite the readout showing 4813). It's an odd thing to cut out, especially because it's so immediately evident, but next to the post-Hammer-Down protocol naming designations, that seems like a small indication of what we could be looking at, although that is as much as I'm willing to stretch about really obscure comparisons.