Your result of $-2089$ looks like you're subtracting digit by digit, but putting a negative digit two in the thousands position at the end where you subtract 8 from 6.
However, this doesn't work, because when you write $-2089$, the minus sign applies to all of the digit positions, so the 8 tens and 9 ones suddenly get flipped to negative tens and negative ones, which has no justification.
Note that $(-2000)+89$ does equal the true result $-1911$.
If you want to start by subtracting 6 from 7 and borrowing, what you should to at the left edge of the subtraction is to keep borrowing from the "empty" ten-thousands, hundred-thousands and so forth:
This leads to a representation known as 10's complement, where a negative number is represented as starting with an infinite-to-the-left sequence of nines. This works in the sense that $...9998089$ does represent the number usually written as $-1911$: Namely, if we add 1911 to it, it becomes 0:
with an infinity of carries disappearing out to the left and leaving every digit of the result as 0.
10's complement is not much used in practice, but the equivalent idea in base 2 (2's complement) is widely used to represent arithmetic on negative integers inside computers.