I'm not familiar with Tetris specifically, but for a score display it was rather common to store each individual digit as a tile ID, which helped to speed up drawing that score into the nametable. I wouldn't be surprised if the algorithm that handles score addition was a simple loop that doesn't check the bounds of the highest digit; this would cause it to eventually corrupt adjacent memory in RAM.

Edit: the article covers much of this! Based on the 3 byte display I'm guessing it is indeed BCD as others have noted, with slower software routines to get around the 2A03's lack of a decimal arithmetic mode. The slower operation may be part of why the crash is possible, but the mechanism is simple unguarded lag: NTSC isn't going to wait around forever and the program wasn't prepared for this.

I’d have to double check a screenshot but it’s likely the largest number that can be displayed in the area given for the score.

It's likely it's 3 bytes of BCD (binary coded decimal). It's a handy way of storing things like scores, especially on 6502 processors which have built-in BCD handling support.