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#Haskell, 154 149 147 145 128 120 119 bytes

import Data.List
(r%x)n|n>0&&r>[]=[(r\\t)%(x++(show n\\t))$n-1|t<-tails x,isPrefixOf t$show n]!!0|0<1=x
h=['0'..'9']%""

adding in the recycling-checking cost a lot of characters... sigh

golfed a bit by remembering what digits weren't recycled yet and stopping when the list is empty. then golfed a bit more by moving to explicit recursion and a few more tricks.

example output:

*Main> h 110
"110910810710610510410310210100998979695949392919089887868584838281807978776757473727170696867665646362616059585756554535251504948474645443424140393837363534332313029282726252423221"