We develop a search‐theoretic model of financial intermediation in an over‐the‐counter market and study how trading frictions affect the distribution of asset holdings and standard measures of liquidity. A distinctive feature of our theory is that it allows for unrestricted asset holdings, so market participants can accommodate trading frictions by adjusting their asset positions. We show that these individual responses of asset demands constitute a fundamental feature of illiquid markets: they are a key determinant of trade volume, bid–ask spreads, and trading delays—the dimensions of market liquidity that search‐based theories seek to explain.