Running out of data on a travel eSIM is an anticlimax, and that's by design. There's no overage bill, no frantic call to a helpline, no charge you didn't agree to. Data simply stops. Here's exactly what that looks like, and what to do about it.
That's a deliberate trade. Some plans elsewhere keep charging automatically once you cross a limit, on the logic that staying connected matters more than staying within budget. We'd rather you decide that for yourself, each time, than have it decided for you by a meter you can't see.
What actually happens
These plans are prepaid - the price at checkout is the price you pay, with nothing metered afterwards. So when the allowance is gone, your travel line stops passing data. Maps stop loading, messages stop syncing, and that's the full extent of it. There's no automatic top-up charging your card without asking, and no bill waiting for you when you get home.
Most people notice it first as a message that just won't send, or a map that spins without loading. Nothing crashes, nothing errors dramatically - it just quietly stops, which is honestly a fairly clear signal once you know that's what it means.
Topping up
If you're still travelling and want to keep going, buying more is quick: open your account, pick another plan for the same destination, and it installs the same way the first one did - over Wi-Fi, in about ninety seconds if you've got it, or over what's left of a hotspot if you don't. There's no need to reinstall anything or start from scratch; you're simply adding another plan on top of the same line.
If Wi-Fi genuinely isn't available anywhere nearby, this is one of the rare moments it's worth borrowing a minute of someone else's hotspot, or asking at a café - the top-up itself is small enough that even a slow connection gets it done.