Can an unlocked phone be used in Japan?

Say I happened to have a Japanese phone that is already unlocked.

Can I bring this phone back to Japan and use it (say, on a prepaid card?) Or would there have to be a process of re-locking the darn thing again?

That's not a easy one to answer.
What model is the phone?
If the unlock is done by a sim then 100% yes if you use it on the network the phone was designed for.
If the phone was software unlocked like the *Japanese* models sold in China then probably not, or at least not with all the features working. Basic stuff like SMS (which locals don't use) and calling will work but the Local features are all broken.
This is more relevant with the newer phones, not so much the older ones from say 2 or more years ago.
Softbank can push firmware updates for all their models over the air BUT this will brick some phones like the 920SC if it has been modified. It's a bit of a gamble.
There is no re locking process. The phone has been modified.
Basically you need to restore the phone to it's original untouched version. You might be lucky to find a firmware around the internet but just know that it isn't likely to work and will result in a phone completely locked.

I believe the short answer of this is as follows.

If the software on the phone has been modified to circumvent the networks settings (i.e unlocked) then the Japanese features are all broken regardless of network. The phone would effectively at best work how it currently works for you. At worst like that 920sc mentioned it won't work on the original network at all.

If the phone has a hardware mod (hypersim or similar) to unlock then the phone will operate 100% as intended on the network it was designed for.