Managing Liquidity Risk

I work at dealer who trades CFDs and I need some help on how to best hedge illiquid equity positons.
Let's say I have 50 equities and our clients hold more shares than the 50% Average Daily Volume and we have the shares hedged 1:1. What is the best way to hedge these positions so that if our clients dump the position we don't get killed trying to dump the position at the same time? Any help is appreciated.

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