Methods and apparatus are provided for managing classification of packets within a multi-function input/output device, and for allowing the device's classification tables to be cleared in a non-blocking manner. The input/output device conveys multiple communication connections corresponding to multiple physical and/or virtual PCIe (Peripheral Component Interconnect Express) functions bound to software images executing on hosts. The device comprises gate logic configured to indicate statuses of the functions or the DMA engines bound to the functions. When the gate logic indicates a particular destination function is valid, the packet is transferred normally after being classified. A portion of the logic corresponding to a given function is reprogrammed to indicate the function is invalid when that function is reinitialized (e.g., FLR or Function Level Reset). The function's entries in packet classification tables are cleared afterward. When the logic indicates a function is invalid, packets destined for that function are dropped.