Main memory, composed of DRAM, is a performance bottleneck for many applications, due to the high DRAM access latency. In-DRAM caches work to mitigate this latency by augmenting regular-latency DRAM with small-but-fast regions of DRAM that serve as a cache for the data held in the regularlatency (i.e., slow) region of DRAM. While an effective in-DRAM cache can allow a large fraction of memory requests to be served from a fast DRAM region, the latency savings are often hindered by inefficient mechanisms for migrating (i.e., relocating) copies of data into and out of the fast regions. Existing in-DRAM caches have two sources of inefficiency: (1) their data relocation granularity is an entire multi-kilobyte row of DRAM, even though much of the row may never be accessed due to poor data locality; and (2) because the relocation latency increases with the physical distance between the slow and fast regions, multiple fast regions are physically interleaved among slow regions to reduce the relocation latency, resulting in increased hardware area and manufacturing complexity. We propose a new substrate, FIGARO, that uses existing shared global buffers among subarrays within a DRAM bank to provide support for in-DRAM data relocation across subarrays at the granularity of a single cache block. FIGARO has a distance-independent latency within a DRAM bank, and avoids complex modifications to DRAM (such as the interleaving of fast and slow regions). Using FIGARO, we design a fine-grained in-DRAM cache called FIGCache. The key idea of FIGCache is to cache only small, frequently-accessed portions of different DRAM rows in a designated region of DRAM. By caching only the parts of each row that are expected to be accessed in the near future, we can pack more of the frequently-accessed data into FIGCache, and can benefit from additional row hits in DRAM (i.e., accesses to an already-open row, which have a lower latency than accesses to an unopened row). FIGCache provides benefits for systems with both heterogeneous DRAM banks (i.e., banks with fast regions and slow regions) and conventional homogeneous DRAM banks (i.e., banks with only slow regions). Our evaluations across a wide variety of applications show that FIGCache improves the average performance of a system using DDR4 DRAM by 16.3% and reduces average DRAM energy consumption by 7.8% for 8-core workloads, over a conventional system without in-DRAM caching. We show that FIGCache outperforms state-of-the-art in-DRAM caching techniques, and that its performance gains are robust across many system and mechanism parameters.