Jelly, 6 3 bytes
-3 bytes by having I/O as a decimal list of digits.
ṫTṪ
Test suite at Try it online!
How?
ṫTṪ - Main link: listOfDigits e.g. [1, 0, 2, 0] or [1, 1, 9 ]
T - truthy indexes [1, 3 ] [1, 2, 3 ]
ṫ - tail (vectorises) [[1,0,2,0], [2,0] ] [[1,1,9],[1,9],[9]]
Ṫ - tail pop [2,0] [9]
If we could not take decimal lists a 6 byter is:
DµṫTṪḌ
Which you can see here.
This does the same thing, but converts an integer to a decimal list beforehand and converts back to an integer afterwards.