First, some physical sectors are reserved ahead of time, so there are always some sectors on either the trash list or the clean list (or both). In the very cheapest and oldest models of flash drives active sectors are only remapped when written to, so you can end up with the situation you described, with wear-leveling restricted to the small area of the device not occupied by fixed data. These sorts of devices tend to wear out rather quickly under certain (common) use-cases.
However, in the better flash devices the FTL will remap even the unchanging sectors over time such that the wear-leveling is spread across all the device's erase sectors. These devices approach the ideal erase/rewrite limit (number of sectors * rewrites per sector).
For example, assume we have a flash device with five sectors: four visible plus one spare. After writing to the full device there are four active sectors (phys. 1-4) and one on the clean list (5). Rewriting logical sector 3 changes the active mapping to (1->1, 2->2, 3->5, 4->4), empties the clean list, and adds phys. sector 3 to the trash list. Rewriting sector three again with a simple FTL just causes phys. sector three to be erased and swapped with sector 5 on the trash list; none of the other sectors are wear-leveled. With a better FTL, however, the device may decide to place the new data in phys. sector 1, moving the original data for the first logical sector over to phys. sector 5 instead (active: 1->5, 2->2, 3->1, 4->4; trash: 3). This introduces an extra erase operation (on *some* writes), but now the changes are spread across three sectors rather than the original two, and additional writes would be further spread to sectors 2 and 4 as well. The end result is that all the sectors end up with similar numbers of rewrites.