Descending digit sequences

Julia, 30 bytes

n->"$n"join(n-1:-1:0)[1:n]"$n"

This is an anonymous function that accepts an integer and returns a string. To call it, assign it to a variable.

We construct and join the descending sequence from n-1 to 0, and take the first n characters from the resulting string. We prepend and append this with the input as a string.

Verify all test cases online

CJam, 11 10 bytes

q4*~,W%s<\

Try it online. Assumes there is a trailing newline in the input. (Thanks to @jimmy23013 for saving a byte.)

Explanation

At the end of each line is what the stack looks like at that point (using 4 as an example).

q4*  e# Push input x 4 times, separated by newlines. ["4\n4\n4\n4\n"]
~    e# Evaluate, separating the 4's and converting them to numbers. [4 4 4 4]
,W%  e# Take the range of x and reverse it. [4 4 4 [3 2 1 0]]
s<   e# Cast to string and take the first x characters. [4 4 "3210"]
\    e# Swap the top two to get the final result. [4 "3210" 4]

JavaScript (ES6), 55 52 bytes

n=>n+[...Array(m=n)].map(_=>--m).join``.slice(0,n)+n

Edit: Saved 3 bytes thanks to @WashingtonGuedes.