Kaite, welcome to FlyerTalk. There is no one answer that can apply to all airlines in the case of a mistake fare.

Instead, there are several factors which must be considered: Was it a mistake fare, or just a discount special fare that the airline does not want to honor? This airline posts many deep discount fares on its website home page. Another factor is what are the laws of the countries in which the airline operates? Some countries allow airlines to refuse to honor true mistake fares; other countries may not allow this.

As I believe that you may already know, many experienced travelers do not contact airlines to ask about a mistake fare. They just book it and take proof of their booking with them when they travel. Of course, if an airline is allowed to demand more funds from mistake fare customers, they may do so at least up until the time of travel.

Some airlines which are allowed to refuse to honor mistake fares may choose to honor them in certain fares. They do this as a gesture of goodwill. They may not allow any changes to be made to the ticket, however. But it is the airline's choice if the laws of their countries allow airlines to refuse to honor mistake fares.

If an airline seeks to charge you a higher fare, you may be allowed to reject the higher fare and instead seek a full refund of the fare which you paid, with no service charge if the laws of the country allow you this. Then you will no longer have a flight ticket but you will have a return of all of your original funds.

Best to have all proof of what the airline had on the website as the fare you purchased: the airline's confirmation of your ticket at that fare, and evidence that the airline is charging you more.