The other value will simply be overwritten in the case of a hash collision. By just writing to a mapping, your program will not notice that there was a hash collision.
The size of the virtual address space of the state variable storage is 2^256 * 32 bytes.
The chance of a hash collision is not just 'really low' it is astronomically low.
The chance is about
0.00... (70 more zeroes here) ... 001%. You are more likely to win the jackpot in a national lottery 8 times in a row. There are other things to worry about in life than hash collisions.
This resource may help you learn more: