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This was actually from a personal experience and I was wondering if airlines would react to such an event.

Let's say a relative has died in Poland and I'm in the United Kingdom. I would have to attend the funeral taking place in Poland. This may seem absurd, but would airlines react and perhaps increase the price of the aeroplane tickets, knowing that I will buy the ticket anyway?

The bigger question is how would they know?

People buy plane tickets all the time for all kinds of reasons. You are not required to tell an airline why you are flying, only when and where (so they can sell you a ticket). Airlines do vary ticket prices but they generally do so proactively and less reactively. There is lots of info out there on how they set their prices like here, here, and here.

Depending on the airline, in your given situation you may even get more flexibility or a discount.

You can always buy at the current price, for whatever reason. The airlines already anticipate that you have an urgent need when you book short notice, so typically the prices go up as the departure date approaches (unless the flight is super empty and they want to fill seats)

My wife had to change a flight because a close relative passing away. The airline agreed to waive the change fee but only after she presented the actual death certificate (which she happened to have).

Some airlines will give you a bit of leeway here, but the agents do get to hear a lot of sad stories from customers, most of which are entirely made up, so having some actual documentation can help the case.