First of all, we'll all be long dead before bitcoin approaches the zero-rewards era so for you (and us) this is just a theoretical problem. But in reality it's not a problem at all because, theoretically, at that point the miners would still earn rewards thanks to the network fees and the value of bitcoins should be high enough to sustain the mining costs.
That's right. Our time will come someday. Why did we start raising such questions at this point in time? Did anyone really decide to live to see such times? Huh? Well, confess, who has the elixir of immortality )) But seriously, I don't even think about such things. This problem will definitely not fall on our time, and then another technology will come to replace it, which will displace blockchain.