When there is no signal in the shop
Poor mobile reception in a supermarket is no accident: large buildings, concrete walls, refrigeration and metal shelving. In practice, much of the shopping happens exactly where the phone is least connected.
What works with no connection
The list itself. You can add items, mark what was taken, change quantities, reorder and delete — all stored on the device. When the connection returns the changes are sent and reach everyone else on the list.
You can scan a barcode too: recognising the barcode happens on the device and needs no internet.
What needs a connection
A price the phone has not seen yet. Prices are read from the server, so for a product it has not looked up the app says it has no price rather than guessing. The practical answer is to build the list at home, while there is a connection, and let the prices arrive then.
What the phone already holds does show. The prices of the last three shops you picked are kept on the device for a day, so the prices beside the items on your list are still there at the shelf, with no signal at all.
Joining a new list through an invitation also needs a connection, once.
Why it is built this way
We could have built an app that simply refuses to work without a network — it is far simpler to develop. The decision went the other way: the list is first a local record on your phone, and syncing is a layer above it. So the thing you need in real time, at the shelf, never depends on reception.
What happens to changes I made offline?
They are kept on the device and sent the moment the connection returns. You do not need to do anything, or stay on the screen.
And if the other person edited meanwhile?
Both sets of edits merge. That case was designed for, so one person's list never erases the other's.