There is a certain amount of "getting your ducks in a row" that may be necessary when someone leaves employment very quickly. They may have been fired (despite someone saying X texted Y "I quit", you may have been deceived) or known they were about to be fired. If locks are being changed, something went down - I've had people give notice at my small firm, laid people off, fired people, and though I asked for keys back, I didn't change the locks.
One of the things you need to get in a row is answers to obvious questions like "will X be replaced? Who is going to do X's things tomorrow? Is B getting a promotion because of this?" and so on. A sensible boss will take a few hours to get answers to these things before starting the conversation with staff. They know that some of you know. They hope the gossip is being kept to a minimum. And they'll provide complete information when they have it, instead of coming back 5 or 6 times the first day with updates, or saying "I haven't decided, we'll have to look into that and make a decision" every time anybody asks anything.
Of course, the things staff ask about are by no means the only tasks you have to cover after a quitting or firing, especially an unhappy one. You also have to make sure they don't get their recurring paycheque automatically, possibly issue a final paycheque, do paperwork with various government bodies such as for employment insurance, possibly notify any regulatory bodies that track which licensed people work where, tell or ask the insurance company when their coverage ends, and write up a formal letter telling the person all these things. You might need to take away their computer accounts, email, or work-issued phone, or get stuff forwarded from those, and decide who to forward them to. You need to think of and remember all this stuff, too, all while trying to do whatever it was you had planned for today.
In larger companies there is a written process and there may be someone whose job it is to swing into action in these circumstances. In smaller ones you have one person whose plate is already pretty full and now has to deal with this as well. Plus whatever may have gone down that triggered it all. Satisfying curiosity on the floor may not have got to the top of the priority list yet.
What should you do today? Exactly what you would do if X were off sick today or otherwise unavailable. Tomorrow, if there's been no announcement it wouldn't be wrong to stick your head into your manager's office and say "I'm covering X's stuff again today, right?" If you get a curt/gruff agreement (no eye contact, perhaps an unhappy facial expression or an actual wave of the hand) go back to your station and cover X's stuff and wait to see if more information is shared in another day or two. If you get a more welcoming response (smile, eye contact, "Thanks, yeah, that would really be helpful") then you can try a gentle question like "is there a long term plan shaping up that I can ask about?" But don't be surprised if the answer is "I will let you know as soon as I know."