What to do when visa admission expires during lockdown?

The Proclamation suspends entry to the US of people who have been to the Schengen Area within the last 14 days, other than US citizens and permanent residents, and immediate family of US citizens and permanent residents. It does not affect exit from the US to the Schengen Area, and it does not suspend flights between the US and the Schengen Area (though some airlines might cancel some flights between the US and the Schengen Area due to lower demand due to the people banned).

There can still be direct flights flying from the Schengen Area to the US, as long as they are carrying only US citizens and permanent residents, or their immediate family members. And those flights can carry people back from the US to the Schengen Area. As a case in point, Air China still runs a small number of direct flights between the US and China in both directions, even though a similar ban has applied to Mainland China since Feb 2.

And of course, you can always find itineraries through a 3rd country airport outside the Schengen Area, which will likely be less affected by cancellations than direct flights.

The procedure for getting extra time in the US is different depending on whether you entered under a B visa or under the visa waiver program (VWP).

Most European visitors will have used the VWP. In that case, there is a regulatory provision for an extension of up to 30 days called "satisfactory departure" (8 CFR 217.3(a)):

§ 217.3 Maintenance of status.

(a) Satisfactory departure. If an emergency prevents an alien admitted under this part from departing from the United States within his or her period of authorized stay, the district director having jurisdiction over the place of the alien's temporary stay may, in his or her discretion, grant a period of satisfactory departure not to exceed 30 days. If departure is accomplished during that period, the alien is to be regarded as having satisfactorily accomplished the visit without overstaying the allotted time.

However, it is not at all obvious how one would apply for satisfactory departure. There is no information about this on the main USCIS website, and the USCIS appointment system website says

If you are inside the United States, you can no longer schedule an appointment online using InfoPass for domestic offices.

(See below in the comments for a report from Crazydre that USCIS is referring people in this situation to CBP deferred inspection centers.)

Even if you could manage a 30-day extension under satisfactory departure, it won't help if you are required to remain in the US for more than 30 days beyond the expiration of your allowed period of stay.

Visitors with B visas may apply to extend their stay. Note that the relevant date is the I-94 date, not the visa expiration date. The application is somewhat costly ($370 plus $85 for biometric services), and may not be decided before you actually leave, but filing the application before the expiration of the admission period shown on the I-94 will protect you against various negative consequences of overstaying. It also demonstrates good faith.

If you do not know your I-94 expiration date, you may look it up at https://i94.cbp.dhs.gov.

Yesterday, I noted in a comment (on an answer that has since been deleted) that it might be easier to get to Canada or another country to avoid overstaying in the US. You have now edited the question to note that you intend to do just that. In that case, then, it might be useful to note that it is legally permissible for you to reenter the US quite soon after leaving, although that is subject to the discretion of the officer at the border, and the likelihood of being permitted to do so will probably be fairly small if you've just been in the US for close to 90 days (VWP) or six months (B visa).

Furthermore, there is confusion (even among government officers) about the conditions concerning "short trips" to adjacent countries by VWP visitors, so returning to the US may be more difficult for VWP visitors in this position. Such a person might be able to get a B visa while in Canada if necessary.

The restrictions apply from midnight on Friday. It's not clear whether that means midnight between Thursday and Friday, or midnight between Friday and Saturday. Either way, there is time to get on a flight. Contact your airline.

The ban does not apply to the UK. Can you re-route via a UK airport? Some airlines are waiving change fees - contact your airline.

If you find you really can't leave before the restrictions start, contact your embassy, or contact the US Customs and Border Protection (1-877-227-5511) for advice.

I see such questions pop up all the time and I wonder:

Did you ask the embassy of your country and/or the US border administration? Even if they do not yet have all the answers, whatever they may answer has more weight than anything on here and can be used to defend yourself in case there are any problems with the information. Basically, if you do as the US border guards tell you, it'll be much more difficult for them to find you at fault, even if they told you wrong (that's why e-mail might be smarter than a phone call).

You are almost certainly not the only person in this situation, and they will almost certainly have a protocol to resolve the situation, if not today then in the next days.

I am a little concerned that contacting officials to explain the situation would just lead me to be flagged for prompt enforcement action.

Nope, on the contrary it's exactly what to do.

For Visa Waiver Program (VWP) visitors, per this government regulation (§ 217.3):

If an emergency prevents an alien admitted under [VWP] from departing from the United States within his or her period of authorized stay, the district director having jurisdiction over the place of the alien's temporary stay may, in his or her discretion, grant a period of satisfactory departure not to exceed 30 days. If departure is accomplished during that period, the alien is to be regarded as having satisfactorily accomplished the visit without overstaying the allotted time.

As such, the visitor is to go to the nearest CBP deferred inspection site (a list of which is found here) and request a "satisfactory departure" extension, bringing the passport and any documentation proving the booked flight was cancelled with no suitable alternative available within the admission period.

For visa holders, an extension of status can be requested for $370 with the USCIS.

I had solid plans to return to Europe soon, prior to the expiration of the visa entry, but that is no longer an option.

Whenever visas or immigration are involved, never "simply assume something like this is a fact". Especially if the source is from news media of some kind, or even worse, hearsay.

Consider your conversation here: Oh, so clever ... by web-argument standards. You claim flights TO Europe are canceled, supported with links that don't say that at all. When called out on that, you "yeah-but" a wild arm-wave about deadheading aircraft, but you're not Juan Trippe, you don't know how airlines work. The problem with web arguments is they come off as cock-and-bull stories. Can you imagine having this conversation in 2021 at the immigration desk at JFK with $3000 of air tickets at risk (i.e. the wasted round trip, plus the "gotcha" price the airline will charge you for a last-minute refusal fly-back). I wouldn't want that to be my story.

• Because if your facts are wrong, and everyone else in your situation was able to get out of the US, then it just looks like you overstayed on purpose.

• And the IO would certainly call out why you waited so late to book the return flight.

So what you should do is disregard what you've "heard" and make every best effort to book the travel in compliance with your visa conditions. Spend at least an hour or two earnestly trying to book it. And ideally, work through a travel agent, and if the agent tries and fails, have them give you a written letter to the effect that they were unable. That letter becomes your "get out of jail free" card vis-a-vis the overstay.

I hear you're going to Canada; that's a great example of "thinking outside the box". Now, imagine the backside of that, and your assumptions about travel east were true after all. The 2021 interview goes "Wow, look at your dates. We've had thousands of people in your circumstances just overstay. Why'd you go to Canada?" "To respect your immigration laws". smile "Welcome to the USA."