If you manage your threads in user level, it means that the swapping is done by your application, not by OS scheduler. Each thread must reach some point where he surrenders (or loses) the control to the management mechanism, but that mechanism is also user-level, so if one of the threads is in the middle of doing a system call - your thread management system (and through that all the other threads) must wait until the kernel code is done.
The OS is still active all the time, and may still preempt the entire program, so other processes will not starve, only the internal "threads" you manage yourself. These threads can't get started during that block because the mechanism responsible of starting them is also blocked by the kernel.