Role of the MMU in a Page Fault Swap
In general, the MMU merely notifies the CPU of a page fault. It is up to the CPU to resolve the problem and then update the MMU tables so that the access can be restarted.

The CPU usually resolves the problem by initiating one or more I/O operations to the backing storage, which is usually a local disk of some sort, but in some cases can be a remote disk accessed over the network. If the page being replaced is "dirty" (needs to be written out), this needs to occur before the desired page is read in. This I/O may or may not involve DMA. The point is, this process is too complicated to implement directly in hardware.

It is a key requirement that any processor that supports virtual memory must be able to suspend and restart an access that experiences a page fault. Many early microprocessors (e.g., 68000, 8086) did not have this capability, which made it very difficult, if not impossible.