Call the first digit of a number digit $0$. The digit after that digit $1$, and so on and so forth.
In base $10$, the number $6210001000$ describes itself, because digit $0$ is $6$ and it has six $0$s. Digit $1$ is $2$ and it has $2$ $1s$. Digit $2$ is $1$ and there is only one $2$. There are none of the other numerals.
So it occurs to me that in duodecimal, you can do $821000001000$, which is $6073061476032$ in decimal. In base $40,$ you could do $Z21000...$ something like that, you get the idea. You could keep going, the only problem being not having enough symbols.
According to a graphic I saw on Facebook, $6210001000$ is the only such number in base $10$. I'm wondering: might there be some base in which a number describes itself like this but its first digit isn't 4 less than the base, followed by $21$ and a bunch of 0s with a 1 close to the end?