Why trade illiquid stocks...

First and foremost, it is easier to become a surrogate specialist in a thinly traded stock than it is for a active stock where big boys are in play. One can have a fair idea about who is filling one's limit orders.
Secondly, the considerable money that Value Traders lose as execution costs can go well in your pocket. Several authors quote that illiquid stocks earn higher investment returns, presumably to compensate for the higher costs of transacting. For the tape reaader it simply means bigger catchable moves. Reference:

• Amihud, Yakov, 2002, "Illiquidity and Stock Returns: Cross-Section and Time-Series Effects," Journal of Financial Markets, 5, 31-56.
• Brennan, Michael J. and Avanidhar Subrahmanyam, 1996, "Market Microstructure and Asset Pricing: On the Compensation for Illiquidity in Stock Returns," Journal of Financial Economics, 41, 441-464.
• Pastor, Lubos and Robert F. Stambaugh, 2002, "Liquidity Risk and Expected Stock Returns," Journal of Political Economy.

Reference post: 6 Rules for Trading by the Tape, Rule#1