We propose ecoTLB-software-based eventual translation lookaside buffer (TLB) coherence-which eliminates the overhead of the synchronous TLB shootdown mechanism in operating systems that use address space identifiers (ASIDs). With an eventual TLB coherence, ecoTLB improves the performance of free and page swap operations by removing the inter-processor interrupt (IPI) overheads incurred to invalidate TLB entries. We show that the TLB shootdown has implications for page swapping in particular in emerging, disaggregated data centers and demonstrate that ecoTLB can improve both the performance and the specific swapping policy decisions using ecoTLB's asynchronous mechanism. We demonstrate that ecoTLB improves the performance of real-world applications, such as Memcached and Make, that perform page swapping using Infiniswap, a solution for next generation data centers that use disaggregated memory, by up to 17.2%. Moreover, ecoTLB improves the 99th percentile tail latency of Memcached by up to 70.8% due to its asynchronous scheme and improved policy decisions. Furthermore, we show that recent features to improve security in the Linux kernel, like kernel page table isolation (KPTI), can result in significant performance overheads on architectures without support for specific instructions to clear single entries in tagged TLBs, falling back to full TLB flushes. In this scenario, ecoTLB is able to recover the performance lost for supporting KPTI due to its asynchronous shootdown scheme and its support for tagged TLBs. Finally, we demonstrate that ecoTLB improves the performance of free operations by up to 59.1% on a 120-core machine and improves the performance of Apache on a 16-core machine by up to 13.7% compared to baseline Linux, and by up to 48.2% compared to ABIS, a recent state-of-the-art research prototype that reduces the number of IPIs.