The population of Moria during normal times was not that great.
Quote:
[the orcs in Moria] were in fact not very numerous
-UT footnote 11 The Hunt for the Ring
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Moria seems to have been garrisoned rather than settled. The Balrog may not have wanted
too many cohabitants.
Also remember that in Middle earth, the hunting is not entirely above ground. "Things" lived underground too, and I doubt that the orcs would refuse to eat them.
EDIT: Also remember the remarks of Gorbag and Shagrat about "Going to the Pot" are rather suggestive.