What happens if the visa label page gets torn from passport?

You are en-route, not in your own country, and a page of your passport containing a visa has become torn or damaged. You are also not in the country that issued the visa...

If you present your passport for inspection, they will immediately consider if there has been an attempt at forgery...

The obvious indicator is misaligned pages...

. . .

At that point, they will examine the ENTIRE PASSPORT, each and every page...

. . They will then use UV testing and check the intaglio impressions to determine if there are any discrepancies. If your passport clears these checks and no traces of forgery are found, they will then kick off their own due diligence procedure. This varies from country to country, but generally it will include a criminal check and advice from your home country regarding your status. They will then reconcile your visa number with their own computer systems. That takes a long time and you should prepare for that event. Even if you pass all of that, they have the option to bounce you anyway. Or they could let it ride, once my wife's passport became thoroughly soaked in baby formula caused by a leaking bottle, and they let her in anyway. The outcome for these procedures is very situational (except for the US) and cannot be predicted.

To avoid as much of this as possible, you can look inside your passport, commonly inside the rear cover and read the instructions for what to do if your passport becomes damaged.

This will probably mean contacting the citizens services section of your country's embassy and making emergency arrangements. You can well expect that they will kick off their own due diligence procedure and that will take extra time. It's important to note that anyone who inspects your passport will need to start from square 1 and examine each and every page.

Once you have a valid travel document (either passport or emergency documentation) you can then approach the consulate that issued the visa and request a replacement visa. They have the option to refuse or to charge you the full fee for a replacement.

If these avenues fail, you will have to abandon your trip and return to your home country. In this case, when you get back you should file a variance with the issuing consulate either cancelling your visa or requesting a replacement.

Tore the page completely out? You will need a new passport. The pages are numbered for a reason, and most passports contain a phrase like "This passport contains 32 pages".

If this happened in transit you could probably explain it away, but not before starting your travels. The good news is if you take the old passport and the torn-out page back to the issuing embassy they will (probably) give you a new stamp right away. These things do happen.

You cannot travel with it because your travel document (the passport) is now invalid.

You need to contact your country's embassy to get a new passport issued, and then the embassy of the country that issued the visa to have the visa re-affixed to your new passport.

Most likely what will happen is that the Sri Lankan embassy will issue you an emergency passport that will allow you to travel back to Sri Lanka, from where you need to get a new passport and visa.

Having a visa page in hand (even if the visa itself is not vandalized) is not considered valid. The visa should be stamped on the passport and the passport should not be vandalized/torn/have missing pages, etc.