Is it a Self-divisor?
05AB1E, 16 bytes

05AB1E probably has some sort of slice, but I failed to find it.

∞ʒDSÖß}ʒ0å_}ηs&lt;è


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Explanation

∞                [1, 2, 3, ...]
 ʒ               Filter all that satisfies:
  DS                 its DigitS
    Ö                is divisible
     ß}              ßy the original number.
       ʒ         Filter out ^ that satisfies:
        0å_}         0 is å digit of the output.
            ηs&lt;è Trunctuatè by the input.